You're listening to reissue LP's which essentially are equivalent to a file/CD.
The digital setup is "better" than your table setup, so a different cart/table investment might be what's the bottleneck is? Phonoamp is competent.
Until a certain level of table/cart is acquired, you may not hear the nuance of an 50's pressed "golden age" Jazz LP vs a file? Digital is pretty much caught up with LP playback in most areas.
If you're listening to 80'-present Jazz, it's likely been originally recorded digitally.
I'm not a digital convert, though it's great when listening to a proper setup.
I'm sure there are other possibilities, which will be mentioned.