Sufentanil ,
I listen to classical 95% of the time, every sub-genre imaginable from pre-Gregorian chant to avant-garde 20th C. and everything in between. About 2,000 LP's in all, 500 bought new in the 1970's-80's, the remainder bought new and used in the past two years.
I had several 1970's low/mid-fi rigs and for the last two years a pretty high end new rig, not quite at the level of Rushton's or Albert's Walkers but fairly close.
The mid-fi rigs, without exception, made surface noise noticeable. That was the major reason I fell into the CD wasteland for 15 years or so.
The new, high end rig renders those noises nearly inaudible. The most common non-musical noise coming from my LP's is tape hiss, which of course would be prevalent on an analog recording no matter what playback medium was used. The noises you complained of rarely exist in my system, with the exception of a few obviously damaged records. When those noises do occur they are infrequent and at such a low level that they are never distracting, at least to us or to any of our visitors.
I fear this experience may confirm something Albert alluded to, that a commitment to a certain level of equipment is necessary. This is especially true for classical, due to the wide dynamic range you've already discussed. Proper cleaning and exacting setup are also essential, as others have emphasized.
At a guess, the lowest level TT/arm/cartridge that might satisfy you in respect of noise would probably retail (new) for $2000 or so. Better phono stages can also make a significant contribution to noise reduction, since lower quality circuits are more easily overloaded by the sharp transients typical of most such noise.
This may not be what you want to hear of course. It may even be wrong! Cello's suggestion of listening to some of your records on a better system would be an easy way to find out. Take one or two of those new audiophile releases along also. That will tell you a great deal about how much is vinyl vs. how much is your system.