Neutral safety switch

I have a 66 with a 289 and C4 thats been very slow starting lately. I discovered that the wires leading to the neutral safety switch were in contact with the exhaust and may have been damaged, i'm thinking this might be causing the starting problem, as i have checked everything else. Is it ok to bypass the switch with the C4 still in there? I'm planning on a T5 swap in a couple months so i'll have to do it then anyways.

Here is what I've checked as far as the starting problem: battery is very new and working fine, battery cables and all ground wires are new, starter is new (replaced it when the problem started, old starter was working intermittently). Everything was working fine, then all of a sudden it started cranking VERY slow, especially in the mornings or when the engine is cold. I had the starter tested, found it was bad, and put in a new one. the problem is still there, however. I think i'm gonna bypass the possibly damaged neutral safety switch and hope that works. Sorry for the long post, but I'm very confused and this is my daily driver! I need to get to class! does anybody have any other suggestions of things to test? charging system is find and engine is running beautifully, just cranks like the battery is dead (slow, off and on).

i have taken my battery out in the morning about three times since this started happening before i tried to start it. I hooked it up to the charger and it immediately read "fully charged". I don't have a voltmeter but I'll get one and check it out, but i think the battery and charging system is fine. its an optima red top, so it puts out plenty of cc amps

the engine ground wire is brand new, and the wire from the solenoid to starter is less than 6 months old