Its time for a re-write of post #4---- Since the crank relay and fuse combo is located in the underhood fuse box, I don't know how you can hear that relay energize from the cabin. When you said you jumped the contacts (of that crank relay), for sure you removed *it* and jumped pins 30 and 87 ? The ignition key would have to be in the full on position to have any chance of getting the fuel pump to run as well as be able to get the injectors to spit fuel and the coils to fire the spark plugs.
If the engine cranks (with key on), maybe it will lite off. then you pull the jumper out to avoid any possible starter run-on. If your still working on it at this time, keep on a going. I'll look for some more possibilities.
Added info>>> That was relay R12---CRANK RELAY you had been jumpering as well as a positive verification, that the fuse feeding those relay contacts FU8-40A---STRTR is good ?
2nd added info--- If the starter *had* been removed as part of the transmission changeout, was there any chance that you disconnected the *crankshaft position sensor connector* just above it (even by accident) ? As in doing so, might have made it easier to remove the starter. An if you did, maybe *it* did not get re-connected. Without it connected and able to sense crank rotation, no injector or coil spark action will happen.