Tania, I have done this many times and depending what your stuffing is you can do them way in advance and freeze them. Just be sure your mushrooms are dry or they will get to mushy when you bake them. Also if you freeze cook from frozen just allow more time. If you let them thaw to much they will absorb moisture from filling and get soggy. Also as Maryanne pointed out you can cut the bottom to make a flat spot so no balancing act needed. Alternatively prepare the stuffing in advance and keep in frige, depending what you are using and get fresh mushrooms the day before and do the stuffing then. Just be sure they are cleaned and dry before cooking with dry the key word as they will loose that bite and become soggy if not, they have a lot of moisture. Good luck.
I’m certainly not a good one for this, but two things I was thinking: you can make the filling maybe two days ahead; the mushrooms need to be baked just a little before stuffing them because they sweat liquid quite a bit. Not sure about how far ahead. I’m sure you already know to slice the bottoms off enough to make them level to keep them from falling over.