...and I already drained the fluid. What should/could I do? I'm planning to tow it to a shop tomorrow, is this a good idea?

 

Yes this is a good idea. I personally would drop the diff and tap a new plug for it-one size larger if you completely messed up the threads and then have the diff cleaned of any metal shavings.

 

Which part of the plug did you strip? Did you strip the threads or the top of the plug where the wrench does on? If you stripped the threads, then you can do what spyfish told you. If you stripped the top of the plug, then you can have someone weld a nut onto the top and after cooling, just wrench the plug off.

 

If it is the top of the plug, then just use a locking plier(?) the kind that you turn the the screw at the bottom to a certain circumference and then clamp down on the top of the bolt and turn. Word to wise, always undo the fill hole bolt before the drain bolt