Hi Rick,
For some reason I always find you whenever I am looking at a topic that interests me ! Maybe because you are now trying to fine tune your TT system.
Regarding variation of vinyl sound, this can be a topic that lasts many pages! Yes, the pressing quality can make a lot of difference, and probably account for the quality difference that you hear. I know this because I often buy same copies multiple times but with different pressings, different production year/record company even. We can tell this really makes a big difference because you know the recording and often the remastering is the same, so the only difference is the vinyl pressing itself. The thicker vinyl almost always sound much fuller with weight and solid sound stage, no wonder the audiophile pressings are always 180 - 200g. The floppy thin records sound really thin and not focused, even if brand new. Poor pressings often have lots of pops cracks, and maybe even distortion even brand new (e.g. RCA made in the 70s are often aweful), The early CBS and Decca thick vinyls often sound quite amazing if in great condition, so is RCA (180g in the 60s) but for some reason I often find them rather worn, not sure if they are not that durable. I think that may be the reason why I find very old Lps in the 50s-60s sound quite amazing despite the age because they are quite thick and heavy. Also the number of tracks/playing time on each side of the LP matters. if there are too many tracks put on the same side, the sound suffers, as tracking becomes more difficult. The newer pressings tend to squeeze more tracks in (I suppose the technique becomes available then) and when it gets to the inner grooves you can hear distortions, even with fine stylus. Again, older pressings may sound better because there are less tracks on each side.
(I listen to mainly classical and jazz and they often reissue the same thing again and again in all sorts of different reincarnations, thus allowing me to compare different pressings often. Not sure about other types of music though.)
Another very influential one is of course the quality of the LP itself, the same pressing can sound great with a well kept great condition LP but crappy with one that is totally worn (even without scratch or pops etc)
The 3rd one is the recording quality - there is really no escape. If the recording sucks there is nothing much you can do about it. I find some cheap pop music especially irritating with superb stereo systems as it basically expose all their flaws. The fake synthesizer sounds more fake etc. Acoustic instruments sound much better on Vinly. Vocals can be so amazing on vinyl but if the singer cannot sing, it mercilessly expose his/her flaws.
I don't deal with much remastering since most vinyl I get are old but I do get few digitally remastered ones which in general sound cleaner but more sterile. I think the original analogue without remastering usually sound better, more organic, unless the recording is not that great, then remastering may help clean up the sound more, like those old 1940s-50s recordings. That is probably why many audiophile LP releases are made from original analogue take without digital remastering, though I have recently bought some analogue remastered LPs that does not state digital mastering, which sound amazing. A common one is DMM - direct metal mastering
https://en.wikipedia.org/wiki/Direct_metal_masteringThat really can sound amazing, with the clarity of CD but not the sterile digital sound, retaining the airiness of LPs!
I am not sure which one is the most influential, probably plays about equal role on the overall sound quality
Unfortunately, the better your stereo the more likely you will hear the flaws of your LPS, but for the most part, even mediocre LPs sound better than before with an improved system. Some people claim a cheap cartridge works better on poorer quality LPs, perhaps because it is not as revealing? That can be true. A better cartridge, i find, tend to give an expanded less forward soundstage, something more realistic but may actually make a poor recording or quality LP sound weaker, less involved. Therefore a cheap punchy forward sounding cartridge often works better in such situation (e.g. The denon 101/103 MC cartridge ). You might want to try an inexpensive punchy sounding cartridge for these inferior LPs.
Adrian