I've employed two always hungry barn cats, one is 13lbs. the other 16lbs. Even though I feed them in the morning, several times a week they'll leave a DB near the back door. Well worth the investment.
Use starting fluid if you want to blow the head gaskets. 6.2's don't like to start without functioning glow plugs or fair to poor batteries spinning the starter. It probably still has the 24 volt starter & glow plug system. Get a multi meter and figure what's 24 and 12 volt.
I vote for one of three things; valve guides, head gaskets, or rings in no particular order. If the smoke lessens, valve guides. If the smoke smell "sweet" or bubbles in the radiator, head gaskets.
I'd make sure to get documentation from the DMV or whomever in case you've been given bad info. The easiest would be to leave it alone and make a note of the mileage when the new engine goes in.
The proctologist cameras on amazon are pretty reasonable, plus you can snake it down a spark plug hole. If you make the plunge, make sure it has a stiff but flexible wand, not the flaccid type that is used with a cell phone. Good luck with your probing.
If you are talking about darkened headlights, I tried the smoked lenses on my 1990 and replaced them after the first time night driving. Couldn't see sh**.
I am confused, Everything worked, then you pulled the switch? Why?
Are you getting power at the low beam bulb? Unlikely but possible that both burnt out at the same time.
I've only used the brackets on the front & rear diagonal corners of the intake manifold. Sometimes using the end of the head or exhaust can mangle up the valve cover.
I forget if it was my old 6.2NA or 6.5TD that use to eat starters, I ended up extending the wires and used a weather-pak connection for ease of removal.
Was it running hot before you messed with it? Did the replacement sending unit look like the old one? Could have mistakenly installed a sender for an idiot light?
A plus on pulling the cover is you can see if the gear oil has any water in it and can check for any sparkles in the fluid. You'll only be out some silicone sealant and 2 or 3 qts. of gear oil. If you've never smelt gear oil, if it smells bad, it's good.