Part 3. is going to be short, as (spoiler!) I am waiting for parts.
So in Part 2. I said I was coming to the conclusion that it may be ROM problem. Based on the extender card, I built the logic on a breadboard to have the ROM select signals to be able to do a signature analysis.
Well, it turned out that U7 is not corrupted, but completely dead. Looking at its outputs when selected, all outputs stayed low.
The other two ROM ICs had the correct signature so, they can be considered good.
How to proceed? Since I did not find any firmware binary online, I posted the question on the HP group and immediately got the binaries. Very helpful people there, I am absolutely grateful. I also got an offer for a working CPU board, that is my plan B. Simply swapping boards is cheating when reviving vintage instruments :-)
I was pointed to Retro Innovations' adapter to be able to use a 27xx EPROM in place of a 23xx ROM (which is the one in this instrument). It is a very simple adapter, but since it had a very reasonable price I ordered one. It was just not worth bothering with designing the PCB and having it fabricated. I also had a couple of 2716 EPROMS, which I did erase, but for some unknown reason, none of them became blank, even though other EPROMS did, as I used the opportunity to erase all my junkbox EPROMS. Hence I have ordered a coupe of 2716s from eBay, I'm curious to find if they are fakes or not. If they are, Ill use some other higher capacity EPROM, they should work as well.
So this is where it stands now, once I get the adapter I'll see if this makes it work or not. I will continue in part 4.