I've been having a little play with mine this afternoon as well, starting with a switched 3-pin socket on the backplate and earthing the boards. I still haven't decided what to do about the PS yet, but I checked the output voltages on the weedy Suoer one it came with: +/- 21v and an unstable 4.90-5.10v under no load, dropping to +13.06, -12.10 and 4.97 after boot up, with a 20v PP sine wave output, so not as bad as first feared.
I also wanted to see what it was like if fed from an external wall wart, so I used a 12v 1A supply into a splitter cable feeding a multi output board for the +/-12v lines (as per Diablo's photo - I already had three of these and had planned to try one anyway) and an adjustable LM317 module for the 5v line. The combination was fine, so is perfectly viable for anyone wanting to run the device in floating mode. The multi output board couldn't supply enough 5v current to be used by itself, though, as the resettable fuse cut out each time as soon as the FY6600 had booted up. I think the stated 300mA per line output given in the sales description is rather on the hopeful side, but there's certainly no problem supplying the +/-12v requirements, and nothing on the multi-board even got warm when the LM317 module was used for 5v. The 1A wall wart was also more than adequate, and was barely warm after an hour's use.
Back on mains power, I checked the frequency accuracy using a 3GHz counter, cross checked with the oscilloscope, and got quite a tight average -4.65ppm result from 0.1 - 60MHz, against the specified +/-20ppm, so I'm not sure whether it's worth the effort to try to improve on that. I think I can live with making an arithmetic adjustment to set the dialled in value if I ever need super accuracy (which isn't likely).
I also checked for phase shift again, using a constant 5v amplitude, and found that the two channels were only 1.4nS apart after going from 1MHz to 60MHz, although both had also shifted another 2nS along the time axis. I haven't read your explanation of the 4nS discrepancy you found, Chris, but my readings indicate that it might just be a bit of "natural variation" (in a sample size of two).
Back to pondering what more to do (if anything) with the PS in mine now ......
Regards,
Dave