I'm pretty sure he actually used the Marshall 1959 SLP's (Super Lead Plexi's), which is a bit of a different circuit than the JCM800. Marshall's own literature on the reissue of his amp is referred to as the "Super Lead 1959RR". Which is available in the HX Stomp as the "Brit Plexi Nrm/Brt/Jump". Everything else suggested is very very close. Here's a close diagram of his rig: https://guitar.com/rig-diagrams/rig-diagram-randy-rhoads-ozzy-osbourne-1981/
While this gets all the ingredients right, it may still not be the exact signal chain he used. For instance the diagram show's the input to the amp being the normal channel (i.e., not the Bright channel or Jumping the the 2 channels). And if you watch closely in this live video around 0:58 - 1:09
It does look like the Normal channel. So it could be right, at least for a live setup. However he swapped-out Altec Lansing speakers for the stock Celestion Vintage 30's or Greenback's. And that's gonna have pretty noticeable affect on the over all sound that he was getting. The HX Stomp cab equivalent might be the 4x12 1960 T75 (a cleaner speaker) or 4x12 Greenback25 (a brighter greenback), the rest of the tweaking would be between mic choice and the 10-band EQ. And then of course the Double/Triple effect/technique that Codamedia mentioned. That last bit will go a long long way to not just getting his sound but the "feel" of what Randy was doing.
Notice that he used a stereo setup so replicating that would also get you closer. Thank god there fewer pedals to choose from back then and he really only had the Cry Baby, MXR Dist+, 10-band EQ, Grey Flanger, and Stereo Chorus (and some sprinkled Analog or Tape Delay). Trying to run this in stereo could run out of blocks. But there should be a workable config. It's very interesting that his pedal board didn't have built-in delay in the vein of the other effects. When it came to delay he must have really liked the tape echo. That would be one reason delay wouldn't have been built-in. Them suckers where just too damn big to integrate into a board.
Anyway, Good Luck! Would love to hear what you come up with.
