I couldn't find any info on the P2142 SRAMs. From
the picture, they
look like 20 pin parts, if I counted right. If they are 4-bit parts,
specifically 1Kx4, does the footprint look close enough to wedge a
2114 in each socket with an adapter? What about wiring a pair of 6116
(2016) 2Kx8 SRAMs up in the breadboarding area? If that's not enough
RAM, surely a pair of 6264s would do it. Just a 16-bit path to the
bus and a simple address decoder, most likely. It's not original, but
it might get you running until you could track down some P2142s.
It will be simpler to create a small tester for the P2142, just like I
did for the BPROMs ;o)
I confess I'm confused with this board...