Agree with the gas tank/hose/debris idea. I already suspected that. My experience tells me that since motor starts with gas squirt, that it is not electrical or timing, it's fuel delivery. As you all have surmised. So rather than jump a person to the tank, lines, filters, hoses, it's better to eliminate items at the carb end first. Especially if the pump got clogged because of the shake up.
Rusty has already said he is all over the hose/line/filter issue. If he gets the tank out, I'm sure he will clean and inspect as advised. He can do the tests in the mean time, as they do not include old lines, hoses or the tank. If the tests are successful, it will be a happy thing and the cause will be narrowed down.
As for the suction, during the tests, the fuel line is short.
After all is actually fixed and buttoned up again, it will start with some choke the first time. Then float bowl will stay full for a few days for restarts.
Rusty: Jim Carter has a new gas tank for $315. If you see any rust inside or out and the outlet is ready to fall off or is broken, consider buying a new tank. With all the trouble getting out and back in. It's also very difficult to clean/restore and may be expensive. No access and baffles. With a nice V8 and etc., a new tank is the right thing to do. Consider yourself lucky they are available. TF is not.
I would assume you have converted to open drive shaft with a 350/350. Driveshafts come off very easily. Maybe just a partial removal/lean over is necessary. If not, Usually you remove rear ujoint straps, then slide forward a bit to release out of the saddles and slide the drive shaft back, out of tranny and to the ground.