Hey everyone! I just wanted to swing back by and provide an update on this situation.
Between my last post and now, I had explored a few areas in an effort to troubleshoot this bike. On the recommendation of a somewhat local vintage bike mechanic, I installed an aftermarket adjustable fuel pressure regulator, and dialed the pressure up to 50psi. This made no difference however.
The pressure at the fuel rail was still falling off immediately when the starter was released and the fuel pump stopped running, suggesting that (since I knew the pressure regulator worked, and the fuel injectors had shown not to leak) the fuel was flowing back through the fuel pump, perhaps due to a failed check valve/flap. I wasn't sure if the lack of sustained pressure could be an issue, so I installed a check valve between the fuel pump and the inflow end of the fuel rail. The pressure now stays elevated after the fuel pump shuts off, however this made no difference in the overall problem being experienced.
At some point I decided that the Electronic Ignition or the EFI computer were potential culprits and I just needed to spend the money to get replacements. Unplugging each, alternately, suggested that the Electronic Ignition was perhaps functioning properly and so it made sense to try purchasing a replacement for the EFI computer first. It arrived yesterday, I plugged it in, and the bike promptly fired up and idled without issue (other than perhaps being a bit smoky). Throttle response also seemed adequate, although I didn't test it thoroughly. I need to go back through the bike and make sure I've put everything back together properly.
My current assumption is that the fire, experienced by the previous owner, melted through wire insulation in such a way that at least two wires were able to cross and short some portion of the EFI computer. It didn't completely fry the EFI, but did enough damage to cripple it.
So now I have a Flying Brick that is, to be sure, better for the attention that has been paid it (even in areas that proved to be unrelated to the underlying issue). I look forward to having it out of the garage and on the road before long!
My apologies for having taken so long to finally conclude this process, and my thanks for all of the input and advice provided!