Biamping B&W 802 with Musical Fidelity and Bryston

Should you find that the bi-amping doesn't alleviate the problem, here's another option: If you open up your 802's: You should be able to easily find the tweeter section of the crossover. There should be two 3 ohm Vishay resistors in parallel with each other, and in series with the tweeter. If you take one out, that should reduce the output of your tweeter by somewhat more than 2db. Hopefully the assembler left enough lead showing for you to simply clip one, so it can be soldered back whenever need be. I'd see if I could find a higher-end CD player to audition before I went to that extreme though. Maybe even one with a tubed output/buffer section.

I could unsolder resistors, but I’d rather upgrade speakers if be-amping does not work. I already looked at Proac D25 but did not like its bass.It was a bit slow and not very tight. I prefer overall tonality and speed of b&W802. I’m thinking about Audio Physic.
I m planning to get a new CD player. I was considering Rega Apollo, but I see too many used on the market. It’s a little bit strange for a relatively new model. I’m using decent tube preamp so I’m not sure if tubed player or especially buffer would make a big difference.

I'd do the new player, or at least audition one, before any of the other options. I've never had a Rega, so I can't advise you there. I've got a BAT VK-D5, and love it(six NOS Siemens CCa's in the buffer). If your pre-amp is clean, it will convey whatever's fed it, good OR bad. A grainy/glaring/strident signal will be passed without mercy. It's possible you have some poorly engineered CDs, but- more likely that the player is the problem.

I just bought a pair of VTL 100 compact mono blocks (100 wpc in 5 Om I believe). It’s a little bit more than I need for the top and I’m not sure if I can run them in triode mode. After I try them with my speakers I will look for a new source. BAT VK-D5 sounds like a very nice player, but it’s a bit pricy. I’ m planning to spend around 1K.

That should get you a really good player in the used market(stay away from Sony, they can be bright too, un-modded). The newer VTL monos are switchable to triode mode. I'm certain the 100's were either switchable, or easily wireable into triode mode(about 50wpc into 8 ohms).