What to upgrade to?

Bob, if I was making my last big upgrade, I would go out and listen to as many speakers as I can, and it doesn't have to be new. Speakers are usually the biggest and most expensive upgrade and effects everything played through it. Why not spend your savings here?

Since you've decided to upgrade to a new cartridge, this should give you a really noticeable change in sound. With your budget, I highly recommend adding a second arm/cartridge, I never knew how much I appreciated having the option of hearing a record played through a different cartridge until it happened. There's really not one perfect cartridge/component out there, so I feel it's good to have options. 

I have noticed a lot of professional reviewers own and highly regard the Devore Fidelity Orangutan loudspeakers.  They also seemed to favor analogue front ends with them.

I would upgrade my cartridge to either a Koetsu Onyx ($10K) or a Clearaudio Goldfinger Statement ($16K). To me those are the two best cartridges in the market. You will still have some funds left over for Harbeth 40.2's

By far the biggest improvement I have experienced (since my ears are not as sensitive as some other people I've known) are the best-engineered recordings I can find. Reference Recordings, various SACD's (not all!), certain vinyl (again, some good, some bad).
And-"maybe" try to pick up an instrument from a music store and learn how to play. A decent classical guitar is easy on the fingers.
In any case, We had a very mediocre stereo in my parent's living room when I was growing up. A Fisher compact system- receiver with a BSR turntable mounted on top and a pair of Fisher 10inch/2way speakers, skinny wires and basic interconnects. But- with a well recorded album (my favorites were Columbia/NYPO/Leonard Bernstein) the difference was stunning. If that's not proof I don't know what is. Atlantic records were excellent also (Led Zeppelin). Over the next several years digital audio engineering may get even better. Personally I don't know what to make of a turntable/arm/phono stage/cartridge costing more than (let's say) ten grand. I own a VPI Aries-I with a Benz HO-MC and a Luckaschek phono stage. It sounds great and I'm sure there's much better out there to be had, but I don't have an extensive collection of records (maybe 500 or so). Honestly none of the stores I've visited had a SOTA analog rig set up to play, so I've been on the CD-player road to better sound most of my 25-30 years building my system. One thing IS for certain- the VPI "killed" the Thorens I had previously owned. 
As far as a better system is concerned, it's also possible you might have to spend a LOT of money if you want a dramatic improvement instead of an incremental one. I found that out the hard way when I auditioned a $3500 Goldmund DAC over what I had.

Hi Bob, I'm surprised the usual advocates of room treatments have not yet rallied to your assistance yet.

I offer this based on an untreated room.

Included in 'room treatments' is a set of subwoofers. Acoustic absorbers and a distributed bass array (DBA) go hand in hand. There is much to learn about this so I suggest doing some research.

To try and keep this short : Sound left to decay on its own will add confusion and obscure detail and the bass in particular will have many peaks and nulls and needs to be smoothed out.
Getting this right will be transformational with money left to upgrade cartridge etc.

I can state confidently that no amp nor TT upgrade will do what attention to the acoustic behaviour of your room will do. You can blow your whole budget on a new cartridge but will be unable to hear any significant improvement in an untreated room.

May I suggest you read up on this. Toole and Geddes will cover the how and why and AudioKinesis can supply the goods.

When it comes to room treatment you will get lots of ill-informed recommendations. Some, such as add bookshelves, drapes and wall to wall carpets. The above will do more harm than anything! Take the wall to wall carpet for instance. Being relatively thin compared to the wavelength of sound, will act only as a narrow-band absorber and remember there is lots of it, so a frequency response plot will show a high-Q dip somewhere in the upper midrange. This is music information that is now MIA and you're not getting it back. The target here is to achieve a specific decay time across the full spectrum.

This is a fascinating subject and there are free downloads together with an inexpensive microphone that will allow you to do your own measurements. It will also help you position your speakers optimally for best imaging and stage. The DBA will take care of the bass. Should you decide to get professionals in, you will be able to monitor their progress and prevent being oversold.

State confidently when the pro's arrive that you want the T60 to be at 400 ms over all frequencies. (actual time is dependent on size of room)