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And get yourself a scissor lift, especially in your situation.
Ok I'm just going to try and learn something here on this subject. It was my understanding that when filling either the tranny or rear end you take the lower plug out as well as the top plug. Then put in the oil until it comes out of the lower hole, not the top hole. Is this not the correct procedure when changing the differential fluids?
With regard to cleaning off the mess, I would suggest brake cleaner. That will easily clean off all that muck so you can begin to identify the source of the leak. Be judicious with that brake cleaner, it cleans well but it can harden seals, ruin paint etc. a better choice is mineral spirits in a spray can. I was happy to see you used the foaming degreaser, also a good choice. Brake clean does have its uses but be careful. Our funny car driver used to get it by the case and it was surprising the amount of stuff he wrecked with it. The frame was 4130 that was bare so cracks and damage could be spotted and fixed. We kept it coated with WD40 or other stuff so it wouldn't rust. Sam would degrease with brake cleaner and a few errant drops was all that was needed to ruin paint, plastic but I digress.