That fact that so many people have been hacking away at this for such a long time without finding an answer, tends to imply that some RCA receivers don't support a power toggle, which would limit your options to either (a) using two seperate ON and OFF buttons, or (b) using the JP1 "Toadtog" utility to simulate a toggle code. For option (a) you could program the ON code to the regular POWER button and the OFF code to the shifted POWER button (or vice versa).
If you intend to keep searching for codes, randomly selecting VCR codes isn't the way to go, you need a more methodical approach. RCA only uses a few different device codes, so you should limit your search to RCA device codes. The EFC for the POWER toggle button seems to always be 099, so you should further limit your search to that EFC, just vary the setup code that you are using.
Here's a table of setup codes from the URC-6131 and their corresponding RCA device codes:
