At least that tells us something Simon.
May be worth a walk through to see if we can find the cause. The fuel pump can over pressure and over supply the peak injector demand on all systems like this, it's usually modulated by a pressure relief valve that dumps fuel back to the tank, but that's not a fixed pressure.
What they do is have a spring backed control valve that (static) achieves the designed pressure of the system and keeps it at that irrespective of injector demand. Then the spring preload can be altered with a vacuum diaphragm that reduces the spring pressure as vacuum builds in the signal tube going to the diaphragm. That vac tube is taken off from the engine side of the throttle plates, so that when you shut the throttle on overrun the vacuum peaks and results in a drop to the delivered fuel pressure.
It effectively runs as a little mechanical / analogue control loop as a parallel but autonomous system to the ecu mapping. But the ecu still has to take account of and be programmed to work with that which happens in this part of the system.
During start sequence with throttle closed, the ecu will give richer mixture based on temp report from engine (effectively using choke) but it should also get reduced injector pressure as the cylinders start to suck vacuum.
The total fuel delivered should be (ecu+enrichment register amount-the drop it would get from lowered fuel pressure) so if the pressure didn't drop it would effectively give double enrichment, and risk wetting the plugs.
It looks like the fuel regulator valve (sitting with continuos spring pressure closed) may be initially just a bit reluctant to release and so the the planned for fuel pressure drop doesn't happen.
Those four ignition applications may just have given it a bit of a kick ( the normal regulator pressure should prompt it to open as the fuel pump is cycled from turning it on a few times) then when you go to start it the vacuum from cranking can operate it easily.
No fuel will pass into the engine just from fuel pressure as the injectors will easily hold it. But just as the cranking starts to draw vacuum then the exercised regulator immediately drops fuel pressure to give correct start aim mixture.
The ecu won't "see" a fault code as normally exhaust Lambda sensors are ignored during initial start, plus they mostly don't monitor fuel pressure and so won't have any idea it's wrong.
Looking at Guzzi schematic, it seems that the order is tank, fuel pump, regulator assembly, then on to injectors. The regulator assembly has also a return to the tank to relieve pressure and vacuum operation from two pipes coming up from each intake tract to enact it's operation.
Because it starts and runs well when you've initially got it going, that seems to confirm nothing is significantly wrong, just that initial reluctance to modulate fuel pressure. It is, I suppose, the equivalent of the carburettor float needle valve sticking and causing the mixture to be temporarily out of range.
Turning it on and off is broadly speaking the "tap" with a screwdriver handle on an old carb to free the valve
