Thanks for the details Pat. I wouldn't dream of fixing these complex beasts without the service manual, that's for sure...
Indeed! It's nice that so many of the manuals are available as scans, often for free from HP/Agilent/Keysight, BAMA or KO4BB, but sometimes you 'get what you pay for' in that their resolution leaves a lot to be desired. For guaranteed good scans, Artek Manuals is a safe bet - Dave's stuff is top notch in that department, and considering the effort involved in doing the scans, he sells them for a song.
One thing I always try to do is to get an actual paper manual for every piece of gear I get. Scans (if clear) are great to have, but nothing beats the huge fold-out schematics in the original manuals, and I find it much easier to flip back and forth with paper pages rather than scrolling hither and yon constantly with a scan, especially for something like the 5340A where roughly the last quarter of the manual is all fold outs. Yeah, you can print scans, but then you often get to play cut-and-paste to put the pages together if it's going to big enough to be legible.
Now that you have the adequate extender board you will be able to work much more comfortably but from what you say indeed it looks like it's a done deal sadly 
Yep. Now to clear the bench a bit and get back to it...
I am starting to get the impression that this particular model is well known, and not just in the US, so maybe at some point, as people collect them, there will be enough people affected by this problem to warrant a collective effort in designing a replacement. This RF stuff is a specialist job of course but maybe there are enough collective knowledge in this forum or out on the web, to allow one to embark into designing a replacement...
That would be a nice little project for RF design aficionados ! Maybe we could ask Shariar/ The Signal Path, and Alan / w2aew what they think of it from a design perspective, if it's feasible or not, realistically... that could make for an interesting video for them to do ! 
I think I might contact them about it... both being in the US, I guess it would not cost too much for someone in the US, owing on of these machines, to ship it to them (along with the much required extended card of course, and a copy of the printed service manual if not available in PDF form for them to download). They have the academic and practical knowledge to tackle this, or at least provide us with a well informed insight, as well as the expensive equipment required to play with this thing at will.
Hell... the two of them know each other, why not combine their expertise in a joint video ?! A co-produced video... I guess they live too far apart from each other to actually meet physically, the US being a vast place, but they could still communicate via e-mail to discuss this.
That might be an interesting project for one or both. I need to dig a bit more into what that IC does in the circuit; perhaps there might be a simple modification that would enable something modern to be used in its place. That would be nice, if so! If the replacement board I got has the same issue and doesn't fix it, I will likely start with an inquiry on the HP mailing list to see if any of them have any ideas.
I just downloaded a copy of the service manual... sadly 99% of it is impossible to read, the PDF is massively corrupted somehow. I could only figure out a few snippets here and there, but OMG I see that this instrument came with GPIB ?!! 
And the manual is date 1975 ! Sure, HP invented this bus so I understand that they were the very first to implement it on their instruments, before other manufacturers adopted it, but still, 1975 ?!! There was not even an 8 bit micro to run such a thing back then, I think ! Had a quick look on Google to refresh my memory, found an article from 1974 announcing a super duper 4 bit MCU...
The PDF was really too fucked up so I couldn't see how they did it... my assumption is that they did not use an 8 micro which did not even exist probably, or elese they might have used it to control the front panel and give their instrument a competitive edge in terms of user interface.... so my guess is that they designed their own stand-alone bus controller, a big state machine, which would not necessitate a micro ti run it ? I am intrigued !
I just did a quick search of my usual spots (Keysight, BAMA and KO4BB), but none of them seem to have a PDF of the manual, so apparently there's no easily available clear copy.
The HPIB apparently debuted in 1972:
http://www.hp9825.com/html/hpib.htmlMy understanding is that in fact HP got into the computer business in an effort to provide automation with their test instruments. Ironic that 30-40 years later the tail grew so big that it parted company with the dog and went out on its own.
Also saw that this beast is really complex, found a snippet about a PLL ?!
That machine was indeed a marvel of engineering compared to my French nixie counters or the same era !
I want one of those, definitely, working or not !!! 
Yes, it never ceases to amaze me just how much they were able to do with what technology they had. Those early instruments are stuffed full of circuitry, unlike modern stuff where there's one IC with a gazillion pins & 37 character long part number, an LCD screen, and a power supply inside an otherwise empty enclosure (ok, I know that's something of an exaggeration, but not
TOO much of one!)
I hope you manage to find one (working, or at worst only needing minor repair). It is certainly a very fascinating piece of hardware! I believe it was introduced in 1973, and at the time had a list price of $5300.00. Add another $400 for the OCXO, $100 for the inputs on the rear panel (useful for fixed test setups in racks, I suppose), and another $350 for the HPIB option. It was not cheap, which is likely why so many still exist - it's built like a tank.
http://www.hpl.hp.com/hpjournal/pdfs/IssuePDFs/1973-04.pdf-Pat
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