Question...

How might one go about getting a totally stripped screw out of a dalek's base? The dalek in question is the Dalek Supreme from the original dalek collector's set.

Drill it out.  take all the other ones out then drill it until the head pops off and yank the base off, that is the only way I know of, or if you can get one of those drill bits that cores into a stripped screw and then undoes it, that is the other way to go.