You can loosen one of your temperature sending units. They're on the 2F head, next to the carburetor. Should have a single wire hooked up. Loosen the sending unit, enough to allow the air to escape. A little bit of coolant might bubble out, and thats ok. I've burped my 2F a few times this way.
Tow bar. No need to remove the drive shaft. Just put both transmission and t-case in Neutral. Get yourself some magnetic trailer lights and you should be good to go.
I've towed mine this way many times behind a first gen tundra and a 2000 F-150.
It's not so much the towing vehicles ability to...
I like that. I pulled my after market gauges out(tach and vac) because I thought they looked way too out of place. You're solution gives me reason to reconsider having them. Nice work.
How are they mounted?
I would check that everything related to the starter and ignition is grounded properly. Including that little condenser.
I had a similar issue, but I honestly can't remember what the cause was and how I fixed it. I did install a @Coolerman fusible link, which negated the the auto zone inline...