Starter issues

11.8 volts is too low.  You should read 12.6 volts at the solenoid.  I'd start by checking the ground cable from the battery to the frame.  Clean all contact areas and dope with dielectric grease and tighten the connections.  Your solenoid is not getting enough voltage/current to throw solidly, thus the  arced contacts.  When you're checking the wiring, check to make sure that the wire from the battery positive terminal to the solenoid isn't corroded or has broken conductors.  The starter takes a lot of current and a wire that is deteriorated won't be able to handle the current draw, even though a voltmeter may show that full voltage is passing. 

You said you twisted the wires together at the clutch interlock switch – did you clean them and use a wire nut or a crimp connector or did you just twist the corroded wires together and wrap a piece of tape around them?  I'd suggest soldering them, since those wires are undersized as it is.

On my tractor, I added a 12 volt, 40-amp relay to the starter solenoid circuit.  Just open the circuit between the key switch and the solenoid small terminal and hool the wire from the key switch to one leg of the relay coil.  The other leg of the coil goes to ground.  Then run an 8 gauge wire from the battery positive terminal to one leg of the relay's switched contacts and the other leg goes to the small terminal on the solenoid.  Now when you turn the key it closes the relay and lets plenty of current flow to the solenoid through a heavy enough wire to ensure that the solenoid is getting all the current it needs for a positive action.

the relay is the way to go it takes care of several issues.

I'm not sure how much more detailed I can get on that relay hookup.  Let's start with the basics:  A relay is an electromagnetic coil that pulls a pair of contact together when current is applied across the coil.  There will be four contacts on the relay – two for the load and two for the coil.  You want to use the old wiring to activate the relay coil so it can then switch current from a better source to the original load.  Therefore:

Obtain from your local auto parts store a “universal 12v 40-amp relay”  This should only cost five or ten bucks.  While you're at it, pick up four crimp-on spade connector terminals, two for 8-gauge wire and two for 14 gauge wire, and about six feet of 8 gauge primary wire.  You don't need to worry about mounting the new relay – it can just dangle from the wiring or you can zip-tie it to something handy, it doesn't matter much as long as the terminals don't inadvertently short out on anything.  Now to do the actual wiring:

Disconnect the wire from the small terminal on the starter solenoid – this is the wire that carries the current from the key switch (by way of the clutch interlock switch you have bypassed) to the coil in the starter solenoid.  The starter solenoid, by the way, is really a relay that switches the power for the starter motor.  We're just going to add another relay in front of that one to allow it to draw more power from the battery.

The wire that you disconnected from the small terminal on the solenoid now is connected to one of the coil contacts on the relay.  The other coil contact is wired to ground.  Now, when you turn the key switch, current is directed to the coil of the relay and that energizes the electromagnet that pulls the relay's contacts together, just like in the starter solenoid.  So the next step is to wire up power to the relay contacts.

Take a piece of 8 gauge primary wire and hook one end of it to the positive terminal of the battery.  You can go all the way to the batter itself, or you can hook it to the end of the positive cable that runs from the positive battery terminal to the starter solenoid big terminal.  The object is to have a source of power that will withstand a heavy load.  Having done that, the other terminal of the relay load contacts is wired to the starter solenoid's small terminal where you removed the wire from the key switch earlier.  Use more of the 8 gauge wire for this connection.

That's it – you should be all done.  Now, when you turn the key switch to the “start” position,  power is delivered to the coil of the new relay, pulling the contacts together to switch power from the new, heavy wire you ran to the starter solenoid’s coil input.  Since the coil can now draw all the power it needs, it will switch very positively and the starter will promptly spin up and start the engine.

Nah, I don't think corroded clutch switch wires alone will cause your problem.  I think it's a combination of things, that being only one of them, along with bad ground, undersized wiring, etc. 

I doubt that you really need new battery cables; just clean and re-tighten all the connections using a dab of dielectric contact grease on all of them.  if you do want to replace them, I'd use either #1 or #0 – bigger is always better. 

Putting that relay in the solenoid circuit will make a huge difference, believe me.  Doing so solved all the starting issues on my tractor, once and for all.  Mine now starts within two seconds of turning the key, every time.

Wills,

Sounds to me as if you may also have a starter that needs to be taken apart and cleaned.

RonJ

A starter and alternator shop would be the most likely source of brushes.  Failing that, I measure the old ones and figure what they would have measured new and go searching online. Ebay, McMaster_Carr, etc.  At times I've had to get brushes that were oversized and sand them down to fit or even modify the springs on them.  That can get tricky but it is possible. 

The commutator should be polished with crocus cloth until it is shiny and then the grooves between the commutator bars cleaned out with a small scraper or engraving tool. 

Glad to hear it is all fixed up and starting well, Wills!  I'd still recommend the relay in the solenoid circuit, as the OEM wiring is a bit on the small side and it can't hurt.  Your call, however, since you're happy with the way it starts now.