Transmission fluid

That is the only method I see. Were you using the special tool?
I see it is a square type plug, like on differentials. I do not know if it is a 3/8" drive though, but I do know when using a 3/8" ratchet sometimes that little ball messes with you and causes the tool to slip or it is not a 3/8" at all. No matter even if you did manage to get any fluid in how would you know if it is full or even overfull? I think you should work on getting that plug out.

I was told it was 5/16 square socket which is what I used, it fits perfectly in the drain plug which to my understanding is the same size/type of plug. Any suggestions on how to remove the stripped plug?

Well, you cannot exactly drill a hole in it and use an easy out. I can think of maybe one or two ways, if something like JB Weld will not work to weld a tool to the plug, then maybe actually using a mig welder and weld a tool to the plug then try to remove the plug using the tool.