At this point, I think I'd try a jumper in place of the fuel pump relay (pins 7&8??), then go drive the car. That would eliminate most of the electrical concerns. If it still stumbles while driving, then put a voltmeter on the fuel pump power leads (use a long piece of speaker wire) to watch voltage AT the pumps while driving.

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There is a very fine line between "hobby" and "mental illness."
FrankenBenz: '87 560SEC with an '02 cammed LS6 and custom 4L60E.
Bling: '87 560SEC, ported/polished, lowered
Lisa: '87 560SEL, lowered