Oppo BDP-95 sounds GREAT?

I can't offer a specific suggestion on the below $100 limit but you could source 5 or 6 feet of power cable and the 2 end terminations and build your own (DIY) for under $100. It doesn't take but 20 minutes to build one and you have little invested to see if maybe just getting a larger gauge cable than the stock one provided gives you something beneficial. You can even go to HD or Lowes and get a 25 foot industrial grade (12 or 10 gauge) extension cord, lop off 6 feet and try it that way. I own the Oppo 95 and use a Shunyata cord (used price was well over $100) but I have used my own builds in the past that cost me less than $100 with good results.

Burn-in would require at minimum for the unit to be turned on - this should have some juice running much of the circuits but probably not all. I would imagine that most people would advise that burn-in truly only happens when the unit is playing. If you want to burn-in while "playing" and not spinning discs then you could always download some music onto a USB thumb drive and let it play on repeat - this might get you pointed in the right direction.

As always YMMV and I defer more of a technical explanation of this process to those more learned than I....