Thank you for the advice. I’ll check these things tomorrow after work and report backAt this point, I don't think shooting the parts cannon at it is the right thing to do without a bit more diagnostic work. Can you check the starter itself with a multimeter, placing the red probe on the big terminal that leads to the bus bars on the firewall and the neg probe on the case of the starter or the transmission? With the ignition cylinder in the on and off positions would help us identify whether or not your relay mod might have an issue. If it's getting 24v to that terminal with the key in on and not start, then you would want to check the relay you purchased and installed in the dash. If it does not have power with the key in the on position, buddy crank it a couple times over so you can establish power in start, then have buddy turn back to on, then back to off. You'll want to check to see if you still have power once buddy turns back to run for a second before he hits off. If you do have power there in run after start, then you will want to check your relay mod.
EDIT: The small terminal on the starter solenoid as well. That will help establish if the electro-magicals in the solenoid are turning off when they are commanded to by turning the key back. If there is still power there once you turn the key back to run, you'll probably want to look into getting a replacement solenoid or starter back from where you got this one.