Jrw40,
This phenomenon is well known and is usually called "inner groove distortion" (clever, huh?!). It exists not because of compression - which would actually tend to relieve the problem - but because the progressive shortening of inner grooves requires that modulations representing any particular frequency get progressively smaller and more closely spaced. (IOW, linear groove speed past the stylus steadily decreases, so smaller/tighter groove modulations are required to move the stylus at any given frequency.)
Since your stylus can't get smaller, nor your cartridge suspension more compliant, tracking these progressively smaller and tighter modulations becomes progressively more difficult. The first audible signs will be distortion and/or disappearance of the highest frequencies. The greater the amplitude, the worse the problem. As the stylus tracks further inward these problems will continue to move down the frequency scale and incorporate more of the midrange.
If all of the excellent suggestions above don't help, the solution might be a different cartridge. Some are definitely better than others.
Doug