Help with CD player 1000

Hi all..

I am looking for a CD player for use with my Stax Omega phones. Since I've dropped the cash on the phones, I want a good sounding CD player, but I really would like to keep the cost around $1K. Here are some ideas.. any opinions?

Theta Miles Balanced
The Stax amp is fully balanced, and I like the idea of a fully balanced cd player. Also of use would be the analog gain controls since the Stax amp doesn't have a remote - and these phones are generally listened to while laying in bed. On the bad side.. the analog gain stage (if it cannot be taken out of the signal path) and the fact that this is quite old technology.

Arcam Alpha 9 or cd 92
Obviously, the ring DAC is the big thing here. On the downside, it isn't balanced, and I wonder about the quality of the power supply (I've heard they can hum, and get hot).

FMJ CD23
More expensive than I would like, but I get the ring dac and a better power supply. Still not balanced. Because of all the press, I wonder if a used one at $1400 is really much of a deal - everyone wants this player.

Assemblage 3.x and cheap transport
Still more expensive, but now I get fully balanced analog. But I'll have more cables (and thus jitter), etc..

What do you think?
-Adam