When I jump the fuel pump relay and crank over the engine I get nothing but an occasional "poof" from the exhaust.

If you "jump" the fuel relay by unplugging it and jumpering from terminal 30 (red wire) to terminal 87 (yellow/red wire), you will run the pumps OK — but there will be no power to terminal 87b (blue wire) to energize the Lambda relay out on the left fender rail.

No Lambda relay means no Lambda ECU power, no Frequency Valve operation. Meaning no fuel mixture control to the fuel distributor and injectors.

To fully bypass the relay, you need +12V on the blue wire, as well as the yellow/red wire.

But IMO, your problem is more apt to be something as simple as fuse 13 (dirty contacts), which powers the fuel relay coil.
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Bruce Young
'93 940-NA (current), 240s (one V8), 140s, 122s, since '63.