I love the PS/2s I have 10. My Model 50 has a working (when last tested) HDD and a dead FDD. I would never recommend someone get into them though. When I first got them in the early 2000s the drives were much less likely to be dead and parts were cheap. Now it's a different world. You really need spares to keep these systems going. I think you have the right idea, try to cobble together a working system from more than one system.
I recently looked into the chipsets of these things, and almost everything is a custom gate array with no documentation. A few chipset mfg. cloned the chipsets but i have yet to find out if they were used in any systems.
I don't know when IBM started work on the PS/2, '85 sounds about right. But the AT was doomed from the start. They crippled the speed to 6MHz, when 8MHz parts were available from Intel. There are dozens of articles in PC Mag/Infoworld/Byte explaining how to run it at 8MHz. The poor quality CMI HDD also screwed them on reliability. In '85 you could pay a premium for a 6MHz IBM with a HDD that could die at any moment, Or pay less, get 8MHz and a normal HDD. Yes you could say they lost control of the market with the first clones of the PC/XT, but these decisions with the AT really helped their decline. Think it was '86 when they finally got around to the 8MHz version. The PS/2 is often described as a failure and the AT as a success. In some ways though it was the AT standard (that went on for years), that was IBM's downfall. I read somewhere that while the PS/2 line didn't set the standard, it was a financial success for IBM.