"Are you saying that its different circuitry (in the crank position) that actuates the relay?"

Yes -- it's the ECU in each case, by providing a ground to the Fuel relay coil, but with different parameters. For cranking and running, the ECU must get an "Ignition OK" signal from the ICU.

I'm not that familiar with 700 ECUs, but the early LH2.4s on 240s had failures with that special ground.

My suggestion (what I'd try) is to open the fuel relay case and put some folded-up paper between the relays (holding the fuel relay armature closed). If you look at the relay with cover off, and terminals pointing down, the fuel relay is on the left.

Then put the cover back on (for ease of handling) and plug it in. The pumps should run immediately, so try starting. IF it starts, the ignition and injector circuits must be OK, narrowing the scope of the search.

(NOTE: this is an untried effort to duplicate the 240 fuse-jumper test that is done routinely. I'd do it with no hesitation on my 940, but you should consider this note as a disclaimer of sorts.)
--
Bruce Young
'93 940-NA (current) — 240s (one V8) — 140s — 122s — since '63.