AC Power - two circuits better than one?

If this was me and rewiring is not an option, I would look into getting a power distribution center such as a PS Audio Premier and plugging into the one 20-A outlet and seeing if all my gear can be accommodated. It is always better, IMO, to limit the number of audio outlets to as few as practical to reduce ground loops and EMI/RFI.

If one power center isn't enough (monoblock amp draw, e.g.) then I would look to get another power center or an A/V grade power strip and plug it into the outlet without computers or motors on the circuit.

The advantage here is that you don't have to worry about phase leg anomalies (etc) because the power generators will scrub the power input.

But if rewiring is not an option due to cost, then my suggestion makes no economic sense because you can rewire for a lot less than the cost of one PS Audio Premier, let alone two.

Usually it is not problem to have video equipment on the same outlet, as most folks are not using both at the same time.
(Though I watch some Sunday football games with the sound off while listening to my stereo)
I have a huge pile of stuff on one 15 amp outlet, and do not have a problem.
IF I were you, I would put ALL the amplifiers/preamp/ receiver? on the 20. and everything else on the 15 and skip the last out of phase outlet.
I have all my amps/pre/receiver/Plasma from a Furman REF20i, and all my other stuff (digital) from a Monster 7000SS signature

Thanks again for your input folks! I will endeavor to load as much as I can onto the 20amp outlet & the remainder onto the 15amp outlet. The difficulty is just physical connection - too many things for too few outlets (in the wrong places!). At a certain point daisy-chaining power strips - & running long power cords - starts to get problematic. That's why I was considering connecting the TV & DVR into the out of phase 15amp outlet.

I was planning on connecting the audio gear via a Monster AV2000 SS & the HT gear via a Monster HD3650. I would prefer to connect the mono blocks & power amp directly to the 20amp circuit via PS Audio duets to avoid the power limitation problems of surge protection/conditioning...

Unfortunately, the configuration of outlets in the room on the same leg isn't exactly convenient.
12-12-10: Salmonsc

You could hire an electrician to move the circuit/s to a breaker space/s in the electrical panel so they would be on the same leg.

Cost?
It won't take an hour but that is usually the minimum charge.

Actually, I had an electrician in on Friday - but as I wrote in my original post, rewiring is not a possibility. It's a very old house & not mine.