Have you tested the fusible links that come off the starter solenoid??Since one leads to the ignition switch, another to the coil/TFI module,etc test them with a voltmeter to make sure none are blown.The picture below will help with their locations.
(Engine fires briefly but dies immediately when the key is released to the Run position)
Crank the engine & when it fires off, pull the small push on connector (red wire) off the starter relay (Looks like it is stuck on a screw). Hold the switch in the crank position: if it continues to run there is a problem with either the ignition switch or TFI module. Check for 12 volts at the red/green wire on the coil with the switch in the Run position. Good 12 volts, then replace the TFI. No 12 volts, replace the ignition switch or check for open in wiring/blown fusible link between switch & starter solenoid.You know the switch is good(most likely)since you just replaced it.
D.S.S. 331 10.5:1
Trick Flow Top End
80mm maf/70mm tb
1 5/8" Longtubes
Cat Hpipe/2 Chamber FM