It's been done, and documented thanks to us. The ECU between the Galant and the Eclipse use identical connectors for both the M/T and A/T ECUs. The M/T ECU only uses 3 connectors whereas the A/T ECU uses 4, ironically enough 3 of the A/T connectors are direct fit to the M/T ECU.
No need to swap harnesses if you don't want to, you can re-pin your stock Galant harness to that of the Eclipse ECU, or buy a conversion harness.
You will not want to remove the lamp indicator for the CEL, this can be useful (knock on CEL feature with Big Maps patch on Eclipse ECU), and also give you a heads up when shit hits the fan if it ever does, prior to waiting to pull the codes. You will immediately throw codes with the 5-spd swap (Valve Body Solenoids, & TC Circuit). If you have to do any type of state vehicle inspections many have failed due to the CEL, so keep that in mind (Also removing the bulb will not prevent failure as they do connect to the vehicle to check).
+rep for you on spreading the word.