Is it possible to have vinyl nearly noise free?

Yes, but there are many qualifiers; some records are inherently noisy due to manufacture; some may have been damaged by kludgey record players in the past. Some noise may be exacerbated by the cartridge and phono stage. 
I'd be hard pressed to summarize record cleaning best practices in a post reply. There are a million ways to clean a record. I guess my observations would be as follows:
1. Do no harm.
2. Get the fluid and contaminants off the record once that job is done. Vacuum can be very effective, but has other issues, including the potential for static and cross contamination, which can be addressed.
3. I advocate a pure water rinse- purity will vary depending on what country you are in and how compulsive you are. This gives you another shot at removing the residue of fluid, which is itself a contaminant. 
4. I know nothing about Gruv-Glide. I don't use any post-cleaning additives; others may have different views.
5. Ultrasonic cleaning brings a lot to the table but for me, is not a compete solution for old records so I rely on multiple methods and steps, including ultrasonic and vacuum.
6. Fluids- pick your flavor. If you are wet cleaning, keep your brushes, vacuum lips, and anything that comes in contact with the record clean during a cleaning session and afterwards. 
7. I resleeve- pick your flavor. Some shed.
8. Static is the devil and I try and minimize it through how I handle a record post-cleaning. I've found it unnecessary to rely on 'zappers' to charge/discharge.
9. I largely avoid dry brushing because I think it creates more issues than it solves. I did find one dry brush I like, but in many cases, you can do touch up (post cleaning, before or after play) using an air puffer, like the Giottos Rocket Blaster. It's around 12 dollars US on Amazon in the States for the large one.

I'm sure there are things others will add. My baseline is how it plays and long term conservation. I have found with some challenged records that multiple cleanings using both vacuum and ultrasonic are necessary. I'm sure you'll get a lot more input. I'm pretty agnostic when it comes to machines and products. That's why I didn't mention any....(except for the cheap air puffer.)

I'll look to see if I have that record- i have a bunch of ASDs, most go unplayed. Was it only released as a 'quad' record? 

@mijostyn-the issue I mentioned about phono stages  has less to do with 'self-noise' of the phono stage and more about how it behaves in response to surface noise, tics, etc. Ralph Karsten of @atmasphere has written at length about that here. 
For stylus cleaning, Ortofon advises against using any solvents that can damage the cement used to bind the stylus to the cantilever. Other cartridges- I think it is worth checking with the manufacturer-- I know Lyra promote a liquid that is safe with their cartridges which I used when I was running Lyra cartridges, but I've only dry brushed (or on occasion, used Magic Eraser or Blu-Stuff, per Peter Ledermann) with my Airtights. My Koetsu is brand new and I've only been dry brushing so far, using a longer bristle brush than the normal 'pad' type. 

I took a quick look and didn't find it, but that doesn't mean much- partly due to how the classical stuff isn't completely organized here. When I moved a couple years ago, I kind of back-binned several thousand records in one room and I go 'shopping' there periodically.
 I also have a 4th dimension problem- you ever experience that? You know you own a particular record, but you search repeatedly and can't find it. Sometimes, you buy another copy if it isn't crazy money. And then, one day, when looking for something else, the thing just pops into your hand?  I really think there is this dimension where records go sometimes.... 
Go ahead, make fun of me. 
:)
Yeah, I remember the SQ/QS stuff from back in the early-mid '70s, whenever that was. I started buying EMI ASDs first for Jacqueline Du Pre, then kinda bought 'em whenever I found them. 
Haven't listened to the Sibelius symphonies in quite a while. Somebody mentioned a Barbirolli of Mahler's 9th here.  I did find that, as a German Odeon. I'm not sure how old it is, it came from a collection that stopped in '91 when the owner passed away. Man, I should get back to listening to classical more. Time waits for no one. 

@mijostyn- I haven’t used an Ortofon since the mid-70s. I will use a bit of alcohol applied to a pad type stylus brush, e.g. the "brush" type Ortofon and many others sell, but I usually only do it sparingly, not regularly, and more in cases of extremis-- for example, I had purchased an old, somewhat valuable record that, despite deep cleaning on the Monks and on an ultrasonic machine (I forget which one, an Audio Desk or KL- I’ve had both), yielded this nasty yellow gunk from the grooves. I immediately cued up; the record was returned to the vendor but the stylus needed to be degunked. That was an extreme situation.
I have in the past periodically used Magic Eraser or the Blu-stuff that Soundsmith recommends, but again, don’t do that constantly- and am always mindful of the forces applied to the cantilever in doing so.
I guess the cautionary note about alcohol could be read as lawyer boilerplate, but for the uninitiated, I’m not sure I’d throw caution to the wind.
I don’t disagree with pressing run variations in quality. There can be considerable variability sometimes among copies of the "same" record with the same deadwax indicia.
On phono stage and cartridge interactions accentuating noise, yes, taken to an extreme, you could conclude that the phono stage isn’t doing its job if it is not handling record tics--that was precisely why I referenced Ralph’s @atmasphere ’s views on this. I do load cartridges for best sound by ear and sometimes it isn’t at 47k.
I was sent some samples of needle drops done on a Sugar Cube. They sounded pretty good. I actually own copies of the early pressings of the records from which they were drawn, so I guess when I have the time and inclination, I could make a comparison, but that might show more about the difference between my more elaborate vinyl front end and the modest digital front end than the effect of the needle dropping software.
For what that’s worth, I have heard archival restorations in studio of very old transcriptions and acetates and despite the effects of digital processing, the sound was vastly improved by the work done by the archivist- the original was a noisy, tinny sounding record ( in one case it was Les Paul acetates cut direct to disc before he got his hands on a tape machine and in another case it was the original transcription discs that Benny Goodman had paid someone to cut for his personal use of that famous Carnegie Hall show back in the ’30s). The digitally processed signal, with painstaking adjustments made by the archivist in tiny time increments yielded a dynamic, very open and vivid sound that was no longer masked in noise. Perhaps extreme cases.
One last note of interest beyond your post- after spending the better part of the day with the one archivist who had the Benny Goodman transcriptions, I returned home to a large dinner party. I mentioned the Benny Goodman concert and one of our guests-- a man of age-- had actually attended it! (He was a youngster and his older brother, who was a big band fiend, had dragged him to that historic show).
regards,
bill hart

Mijostyn- those digital microscopes- at least the cheap ones- are a little tricky. The 'frame' of view with high magnification is very limited- obviously, and care must be taken to mount the microscope in a way that it is aimed properly and doesn't move or get jarred. I use a lab stand and lab type clamps- but I didn't go all spendy on a $400 US one-- they were under 50 dollars US. Maybe the expensive ones are better. You can definitely see a lot more. 
For routine cleaning, i use various loupes- i did a little research on them, most of them are pretty bad, optically, and the claims of 20x-60x are kind of a joke. From what I gather, a jeweler's loupe should only be 10x and have triplet lenses-- I have several. One I use-- i'm getting old-- is a set of magnifying eyeglasses with illumination. It's only 3x, but sufficient for me to see the stylus and brush- i've been using a longer bristle than the pad type, as I mentioned. 
I guess this is all obsessive but I think we agree that keeping that stylus clean as well as the records is pretty essential. One thing I found on my Airtight Supreme, which is now out for rebuild, is that a lot of stuff collected on the top of the cantilever. This, even though I'm pretty fanatical about record cleaning and stylus cleaning (the latter within reason). I also think there's a lot of stuff-- dust, human skin shed, whathaveyou-floating around in our rooms. I have a dedicated room, no pets allowed, no smoking, etc. and decent central air con and heat with good filters. There's still an endless amount of 'housecleaning' to do in that room, which just adds to the stuff that can collect on a record during handling and play. 
regards,