I don't really know where you are at here but rightly or wrongly I can't see how the ignition /kill circuitry would contribute to the starter problem unless somehow it contributes such a high amperage drain worthhy of smoking up the place being low drain elements to begin with.
That said and not to oversimplify as an occasional greenlighter.... if it seems there are no mechanical issues with the engine innards, soexternally your left with few possibilities
- bad starter
- bad power circuitry
- bad battery
Bad power circuitry seems the likely suspect, ohms law and and an inexpensive IR gun are is your friends...incl your fingers ! .
Before doing a series of cranking test and after cleaning all electrical junction points incl. cable crimps..... properly install a voltmeter at subsequent points and note the voltage before (up to the solenoid) and during while cranking.
Each point showing lesser and lesser volts indicates a resistance to current flow and is likely to generate heat (P=VxI across the resistive junction) which your fingers or an IR gun can sense.
main points to check...
- across battery posts to establish a referrence value before/ while cranking
- across solenoid "IN" post and battery B- (before and during cranking)
- across solenoid "OUT" post and battery B- (before and during cranking)
- across starter "IN" post and battery B- (during cranking)
tell us what you found