Dear 1000nuts...
you came to this site for some help - so hopefully folks will provide some guidance.
The transmission - the driving video on BAT does not show the shift knob, so not easy to tell if seller was shifting manually or left it in 4. You can add ATF type 2. Only add a pint or less at a time and add through the trans dip stick. Once you get some fluid to show at right level, then you can see if waking her up helps.
On the BAT video the car seems to start right away - a good sign.
Agree with your notes on fuel and such.
Don't get to caught up until you check the basics.
Need to know if ignition is the factory transistorized or has it been by-passed and running something else - very common.
If you want an expert opinion, and feel like you can drive 40 miles north - you can call and visit Gernold at SLTECH. There are a very few extreme experts on these cars and you are 40 miles from one of them.
I would get it running a bit better, test it around your home to feel you can drive it, and get it to Gernold with AAA card in hand. Ask Gernold, to check it out and give you his opinion on what it will take to make it what you want - just drive great and enjoy or what level you want it. He should be able to give you a full assessment and can advise what it might take to just get it to run good.
https://www.sltechw113.comThe 11 miles you mention might only be cause the odometer stopped. That happens and can restart by fixing the gauge or cable etc.
The heater levers are a pain, but doable - and looks like you got a new set.
Sure, we can all find issues, but at moment, you need solutions - hopefully we can help bit by bit. As you provide more details folks will help.
Best,