CD Player Recommendations - System sounding shrill

Hi. I haven't upgraded anything in my system for several years, and no longer read Stereophile or visit stores, and find that I am really out of the loop on modern equipment. My system currently annoys me as I find it overly shrill sounding, and suspect it is the CD player which was never really up to par with the rest of the system anyway. The system is as follows:

Linn LP12
Audio Research LS7
Adcom GCD-575
Nakamichi PA-7
B&W 802

Astute observes will note that when I upgraded to the LS7 I no longer had a phono stage so I rarely use the LP12 anymore. The system lacks the bass extension that I would expect and believe it is the Adcom, however, I suppose it could be the Nak. Anyway, I wanted to correct this problem, hopefully, without spending a lot of money. My questions are:

1. Does anyone think the power amp is really the problem as opposed to the CD player?
2. CD player recommendations - should I just go with a DAC and keep the Adcom, or replace the entire thing? I was thinking of a Micromega Stage 2 or Rega Planet - as I said, I would prefer not to spend much money. I am shying away from the Planet since it is top-loading.

Thanks in advance,
Todd