New CD player for an Ayre cx-7e

Ayre CDP is a great choice.

Having said that, I am using the Transporter with Ax7e with great result.

Going from SE to Balanced is not WAY better, it's noticeably better, appreciably better, but not substantially better.

I actually tried an AX-7e with a Marantz player (can't remember the model) and, when switched from the single ended to the balanced outputs/inputs, not only way there a more detailed sound and blacker backgorund, about 6db's were gained. (My preferred listening level was 6db lower in the amp volume control when using its balanced inputs). Does this sound normal?

Yes this is normal. When 6db's are gained, your volume level will have to be decreased from what it was as you have gained more in detail and lowered your noise floor which translates into blacker backgrounds as you have described.
As for the anti-cables IC's, keep in mind that they take a long time to break-in(200-500 hrs.with 500 being the optimum) so be patient! A lot of folks aren't and that's why you see some negative reviews on them because they're not given enough time to break-in. They will sound good right out of the box but they go thru a metamorphosis over time(between 100-150 hrs.) where they will sound soft in the bass and restricted in the highs but after 400-500 hrs. they will sound better than any cable out there costing 35- 40times more.

I'm using a Rega Apollo and SlimDevices Squeezebox thru a Benchmark DAC into my AX-7e. The Benchmark has both balanced and single ended outputs which makes it easy to switch back and forth to perform A-B comparisions. I too have noticed a reduction in floor noise and appreciate the difference enough to not even consider using single ended anymore. You will notice that the Ayre is very sensitive to cabling. I'm using Transparent cables and am quite happy with them, so I can't really comment on the anti-cables. I did use anti-cable speaker cables on a tube based system in the past and got irritated at the inflexibility of them (not to mention the very low WAF). I am interested to hear how you make out with the anti-cable ICs.

Just saw a Raysonic 168 FS this morning on AG. FABULOUS! Plus, it can be used direct out which I am doing. The output section is so good I sold a $2900 preamp