Is the disc warped?

I'm by no means an expert, but sometimes you just get a bad pressing. I don't know what would cause the arm to lift on the JVC. At any rate, it doesn't sound like a 'table issue; It sounds more like the record was made improperly.

Sounds as if the record is 'undergrooved' and what you are seeing / hearing can / might be a couple of effects:

Older (more worn?) JVC has a 'blunter' stylus which is (in effect) recognising the undercuts as run out and is reacting accordingly - whereas your new machine will have a 'sharper' point which is more able to get into the grooves, but has a difficult time staying 'in the groove' or reaching the 'bottom' as they are undercut...if all that makes sense...it used to happen a lot on later pressed releases of mega seller discs, and I guess is one of the sublime contributing points which make 'first pressings' so attractive to collectors. (A 'mint' 1st pressing will often play as good, or even better than many later released 'audiophile' grade discs...maybe not so much these days as the quality has improved massively over the years, but certainly for older / rarer discs the one to have is the 1st pressing for sure.)

You could try getting out the sewing box and using a button, place it on the arm exactly above the pressure point of the stylus on either machine - very light button on the new one and / or heavier button on the JVC especially at the groove section where it stops - this, in effect, 'recuts' a new groove. Be very careful if you use a heavy button on the JVC and use it only on the bad section if possible - it requires a very steady hand for placing and removing whilst the machine is working. I would suggest in your situation that you try a very light one on the new machine and just run it all the way on the bad side - I have no idea how to grade buttons, but I guess an easy light would be a kiddies shirt button and a heavy would be a gents cardigan type. This was how I started and eventually worked my way through to having the confidence to go immediately to a coin, depending on the nature of the problem - it works especially well on older records with 'jumps' or badly scratched requiring 'emergency' fix.

Seriously intense cleaning can often help problems such as this also but I am not about to disclose how I used to wash them in the sink with a scrubbing brush, dry them on the dish tray and then sandwich them between two panes of glass in the oven for a few minutes with the chicken casserole...such disclosure would have me in sackcloth and ashes for a long while...pretend that was a typo...ooops... (Seriously though, some good quality cleaning fluid and a slow wipe then brush can work wonders.)

Please note this will not win you any friends amongst the purists who will probably never admit to such tricks, but it does more often work than not and is for sure much better than any faffing around with tracking / skating settings which will never do the same job (in my experience), and either work (or not) very quickly.

I would also suggest if this all fails / responses do not produce any better ideas, you might try raising the issue in the 'analogue section' as folks tend to get into a mind set when using forums, and repairing vinyl is quite, eh, specialised,tricky and extremely debatable...to say the least...I fell sure there will be many reading this with hand slapping the forehead and shouting at me for suggestions such as these from the good old days...tee hee...