Cambridge 840c vs. Bryston BCD-1 vs. Ayre CX-7e

I’m looking for a new CD player in the $1500-$3000 bracket. As my Sonic Frontiers Line 3 preamp definitely sounds best when run fully balanced, I’ve narrowed my search to a player with balanced out.

Besides the much discussed relative merits of the Cambridge Audio Azur 840c, Bryston BCD-1 and Ayre CX-7e, I’d welcome opinions on the following two specific questions.

(1) As my budget maxes out at 3K, would it be better to:

(a) get the Cambridge and splurge on 2 pairs of up-to-date balanced interconnects (possible candidates include: Acoustic Zen Matrix Reference II; PS Audio xStream Resolution Transcendent; Synergistic Research Alpha Sterling Discrete)? or

(b) get the Bryston or Ayre and stick (for the moment at least) with my (original version) balanced AudioQuest Emerald cables?

(2) are there any other balanced-out players out there in this price bracket that I’ve overlooked and should be considering? (For instance, the Cary CDP-1, though it doesn’t seem to have been as well received as my other three contenders.)

Thanks to all.