I'm still suspecting the ignition switch. It's just a plastic rotary switch, it could be worn out.
Next time you pop fuse #10, see if that green wire off ign switch term #15 has +12v even if the car is switched off. I'd think that if that part of the ign switch was melted and it kept the circuit closed, it'd keep the car running even if you turned the key off.
I'd also think that if one of the unloader relays is shorted/damaged (or maybe an incorrect part), it would flow enough current to overload the #10 fuse. I'm told that the relays are always grounded through the starter in 'Run', but the resistance is high enough that the starter won't run. Those relays have built-in resistors that (might) prevent too much current from flowing through the black/green wire.
Could also be the starter. You're sure the terminals on the starter are wired up correctly both internally and externally?