CD player suggestions...

Find an Oppo 105. It does it all. 

I have mentioned I own and am blown away by the Audiolab 6000 CDT, BUT, the OP asked about PLAYERS. I am surprised that no one has mentioned the Project DS3 MSRP $899.00

I had a Oppo 105 which over time I replaced the crappy PS with a LPS, upgraded the IEC with Furutec which had a sliver tail to the PS board, bypassed the 110/220 switch, all to great affect, but it didn't hold a candle to my 6000 CDT using the built in dac in my Audio Alchemy DDP-1 with optional PS5 power supply

Hey @tweak1 

Did you put a LPS on your 6000CDT? If so, what was involved?

Thanks.

@peterpetre 

No. But an interesting idea. Do you know whether they come with appropriate IECs? I may be getting a Project to compare, first

Cambridge Audio CXU is strong contender in your price range, if you can find one. Plays lots of disc types including SACD, equipped with digital outputs in case you want to use it with outboard DAC and pure audio mode which disables all circuits other than audio path circuit for better SQ.