Obviously, being a tube guy, I have listened to a lot of tube players and many of them reside in my personal home system.
RAM CD25 (personal system)
Jolida
Audio Note CDT-ONE w/ONE DAC
Audio Note CD2.1x
I have yet to hear an AH! or Heart but from talking with others, including reviewers. I would also throw these on your short list to audition. The Heart and Jolida received great reviews by Nels Ferre on TNT and the AH! by Scott Faller also on TNT. They are all good pieces and one would have to audition to see which one fits the bill for personal taste (and budget) with all players, other than the Audio Notes being in the $1k price point. I am thinking of picking up an AH! as to be better able to do some comparisons.
Personally, every component must have tubes to reside in my personal system from the source, CD player and tuner, right down to the amplification. I prefer vinyl but not always convienent so tube sources fit the bill nicely here bringing you [closer] to the vinyl sound. I know this is only personal preferance and YMMV.
Long live tubes and vinyl!