Is there any way for me to reheat mini beef wellingtons without toughening the meat?
Very doable, you just have to fool around with them a little.

Watch the meat carefully, and check the internal temperature in several pieces with a meat thermometer, as they're heating. If you're concerned about a hot spot in the oven, you can rotate the pan every couple of minutes. Pull from the oven once they've reached serving temp. Remember they'll continue heating for a couple of minutes once they're resting.