I would use what I call a gear oil sucker to get all the oil out through the fill hole, and fill it up with synthetic gear lube. What I call a gear oil sucker is about the same size as a grease gun. The have a handle to pull a piston up the bore, and a clear plastic tube to insert in the fill hole.

If I decided the get the drain plug out, I'd pull the transmission. I would lay it on it's side, drain plug up. Then I'd find a nut with 7/8" (same as 22mm), and weld through the center of the nut to the damaged drain plug. I'd have my ground clamp on the outside of the nut. After my weld was complete I'd try removing the plug. If it was still stuck I'd hold my welding ground firmly against the bottom of the transmission case adjacent to the drain hole, and do a little welding to the inside of the nut. The welding current flowing through the threads would blow any corrosion out.
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john