1 Lucky Texan

yeah, looks like corrosion at the connection and maybe up under the insulation created enough resistance to really heat up!

looks like someone on ebay is selling singles; https://www.ebay.com/itm/12oz-YIELD-Release-Agent-Penetrating-Lubricant-H2-Loosens-Rust-Instantly-New/123824283059?hash=item1cd4809db3:g:IOsAAOSwxcZc9Fu2

I feel ya on the last part - I raised 3 daughters, trying to keep them and the wife in reliable cars meant I was driving death traps all the time. I drove a 1981 (yeah, '81) Honda Civic wagon for 19 years, most of the time no a/c .

get a used Subaru axle from car-part.com . Reboot it now if you want or, put it on, watch it, re-boot the present one at your leisure if you feel it's OK inside.

without the engine running, there's no pumping action to move fluid...so, maybe there's no pressure on the clutch pack and the drive shaft is just spinning its 'side' of the plates? Still, the trans fluid might overheat 'locally'.... those instructions seem odd.

bad engine temp sensor might be telling the ECU to 'choke' the car all the time....

try driving with and without the fuse.

it isn't good for it. Causes torque bind on dry pavement. I doubt anyone can say how 'much' damage is done.

ztrain - if all 4 tires are not identical, you need to use the FWD fuse. Is the donut still on the car?

if it smells rich when cranking, try HOLDING the pedal on the floor when cranking. That signals the ECU to shut off fuel , it's the 'clear flood' condition.

if at all possible, take it to; http://superiorsoobie.com/

nowadays, I'd think parking garages would have some video surveillance...

well, even mud and wet streets have 'some' traction....just spitballin' try comparing with and without the FWD fuse in. Compare forward and reverse? maybe get a coupla helpers to video from each side to see what's spinning and what isn't? maybe spring for more ice ? lol! I dunno find a spot to do this without 'high centering' ? ;

drop the front tires onto 2 bags of ice? using a floor jack is frightening to me, what if it flipped or you drove off the pad?

without building some type of roller pads like in youtube videos --- just brainstorming some kind of test. be safe if you try something that is gonna limit steering/braking ability!

put the front tires on wet grass or soapy water, or, 2 creepers???, and see if the rear will push the car forward.

new or cleaned PCV valve 'might' slow the leak a little

kinda wondering about a pinched harness or missing ground but, I dunno temp sensor should be on the crossover pipe. Could be 1 sensor for gauge and ECU, 3pin-connector. If older style, there will be 2 sensors near ecah other, one with a single wire for the dash temp gauge, another for the ECU.

cool

uh - I might give SOA a call and ask if the recall should cover those cam area seals.

you could read some discussion here; https://www.subaruoutback.org/forums/61-general-discussions/118361-awd-system-questions.html

I also am in the habit of re-connecting connectors on occasion, in case a fresh 'wipe' of the contact surfaces removes some minor voltage drop. the ecu and all the sensors. solenoids, motors, etc. make the modern car as much an 'outdoor' computer as a vehicle. doesn't mean it will solve the present issue, but is cheap and easy to try.

certainly far from plug and play but, maybe some other small xverse engine could make a fun project? smart car, or honda Fit or motorcycle engine.....? any 3 cyl JDM engines?

to be clear, NO ONE is suggesting shorting the BATTERY terminals in any way. The idea is, disconnect one of the battery cables. Touch that CABLE'S end to the other battery cable's end. yes, you should be cautious doing this as you will still be near the battery , possibly with long metallic tools around, but, it can be done safely.

you also try temporarily adding a ground connection from the TB to a good ground - and look around for ground points to refresh....wire brush every side of every lug, the body/part, the little screw, etc. - then reconnect and maybe coat with dielectric grease.