Thanks for the diagram, that's exactly opposite the diagram that I have so I'm checking the wrong wire. I have a Haynes manual that I haven't looked at in years and the diagram was tucked in there. Maybe I'll finally be able to get to the bottom of this.

I know the jumper was just to troubleshoot, I have been getting myself convinced that the problem isn't with the fuel system but having had the leaking injector originally I've been stuck on fuel system and being able to run the pump when starting gave me the final push to start looking elsewhere.

I'm not sure how many realize how easy it is to force the fuel pumps to run on a 240 as you've shown with a jumper wire, bypassing a possibly troublesome relay or simply just forcing them to run as in your suggestion. Don't have to get yourself dirty, barely needing to open the door. I was very impressed when an AAA(CAA) tow truck driver once said he packed around paper clips just for such purposes, to get a stranded 240 owner going again and home under their own power. (I'd have to double check this as my diagrams aren't handy, if you go hot bottom left to main fuel pump upper left, a paper clip can be firmly affixed into the tab holes to run the main pump with the fuses removed, albeit no longer with fused protection or the in-tank pump, remove it immediately once the engine is off). A later tow truck driver similarly impressed me, saying he knew to try pulling the AMM connector and force limp home mode so people could get home with a bad AMM. Note to earlier K-Jet 240 and 140 injection system owners, it's fuses 5 and 7 that get jumpered rather than 4 and 6 here with the later LH Jetronic. Check the labelling on the fuse panel cover to be reminded of the main fuel pump fuse.
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now

Interesting set of symptoms you're developing here. There are a number of factors you've established:

I'll try to summarize some of the more notable factors as I see them. Everything starts and runs fine with a warm engine. Everything seems capable of functioning okay under normal conditions. An overnight cold start allows the problem to arise. So block/ambient temp and most especially time are key factors that need to be accounted for in solving this mystery. The excessively cold rough running, almost stalling, is suggestive that things may not be equal in all cylinders. And last, but perhaps not least, you've replaced a lot of stuff that might normally be associated with such problems.

Art and I have been on the leaking injector possibility from the start as your symptoms are very suggestive of this, also it's been a topic here recently. That you've replaced the injectors is what led me to ask about a cold start injector (my LH 2.2 didn't have one, just wasn't sure if that applied to all, similar to the LH 2.4 engines, some had them, some didn't). The absence of wet plugs doesn't mean one or more cylinders aren't slightly flooded. Deposits elsewhere in the cylinder could be damp, especially at the valves, especially the intake valve, next stop along the way from a leaking injector. The absence of notable residual fuel pressure in the morning can be considered reasonably normal. Once the pumps spin up enough for it to catch, fuel pressure should quickly return and the engine should not keep cranking or hesitating for more than a moment or two. That's why I asked if it takes longer to catch when cold cranking, which you indicated it doesn't.

As an aside after that last thought, as a quick and easy test and not all LH systems do this, when you turn the key to the ON position (KP-II) the pumps will spin-up for a second to build initial fuel pressure prior to cranking. In a quiet environment you can hear the pumps buzz if you stick your head low by the door sill. If yours can be heard doing this then you can try the following. In the morning, turn the key to the ON position a couple of times to fully prime the fuel system. Does it now start and run notably better? Again, not all LH 2.2 systems do this, but Art has previously suggested that most do. This would then be indicative it's a fuel side supply problem.

I have one new thought as a possibility and that's cylinder compression. A sticky or badly worn piston ring can act very much like this on a stone cold engine after everything gets a chance to cool and leak down. Cylinders and pistons warm faster than the rest of the engine and will quickly expand to seal in a matter of a minute or so, much like you describe, unlike at the block temp sensor where things change more gradually. That also agrees with yours soon becoming normal when warm and stays that way until stone cold. BTW, you changed the correct temp sensor, the rearmost. I would not have put it on my suspect list, just checked the electrical connection in that harsh environment, especially as your is at the tail end of the 240 wiring insulation issues. IMO, these often get unnecessarily replaced. Symptoms of a failing sensor usually show up as increasingly high rpm as the engine warms.

Given all you've replaced and checked, and not having a fuel pressure gauge handy, my next step would be a warm compression check and then a morning cold compression check, both done dry (no added oil), both done with the injectors unplugged. After the cold compression check, now do a wet cold compression check, a half to a whole teaspoon of oil into each cylinder. Crank it a couple of times to work it in, then do the compression check. If my theory is right, you'll likely find a cold compression check shows one or two very different cylinders and for the wet check all cylinders will be much more even and closer to normal. Even more indicative, if I'm right, after doing the wet compression check with the rings now better sealed, re-install the plugs and reconnect the injectors, then try starting. If I'm right, it should cold start and run much more normally, perhaps a couple of stumbles while the oil burns off.

If that's not it then I'd go back to Art's train of thought further diagnosing at the fuel rail. That's too bad if yours doesn't have a Shrader valve like the later LH systems. You can even use a tire gauge on those to get a quick and approximate reading. Harbour Freight and Amazon will of course have suitable fuel pressure tester kits with the needed European metric adapters, but a cheaper solution is of course a homemade setup as you were thinking (I keep meaning to make one). As I recall, Art has published the details for making up a K-Jet gauge with brass fittings from McMaster, either on his website or over on T-bricks. I'm not sure if he's got the details for the needed LH Jetronic fittings.

Failing all that, I'd change tracks and think about the ignition and electrical side. Do double check that all ignition boots (especially the plugs) are fully seating and pull off, go back more or less the same as the others. Problem with reading brand new plugs is they won't show fuel damp carbon as noticeably or have much time to accumulate deposits, especially if it's mostly accumulating at cold starts. You mention a worn distributor oil ring. That's a definite problem area with the rear mounted cam distributors on the 700/900s, but perhaps not so much on the side mounted ones like yours. Should be fairly easy to remove the rotor and plastic shield for a quick check of that lower area with a paper towel. If the seal is leaking that whole area should be oily.

I'll finish by reminding us that weak or partially corroded electrical connections can behave much differently on a cold or damp morning, such as at this time of year. Our Volvo electrical systems are rather prone to this. Maybe check/spin the key fuses just to be sure.
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now