Egan:
If gnomes can *insert arbitrary action* once per day, what is the limit on what that arbitrary action can be?
Why can't the gnomes just magic away all their problems? Why do they even bother hiring an adventuring party to begin with?
See how an inconsistent world quickly falls apart? Unless you explicitly *WANT* a world that has batshit crazy going on in it (like Discworld)-- being self-consistent is very important to successfully interacting with that world.
NFO:
Again, I would personally make it as painless for everyone as possible with a couple simple mechanics:
Borrow heavily from what you need to make a potion-- Materials, mental energy in the form of experience points, a place to work that is controlled, and a time slot to do it in.
Since wizards have to spend the night mentally prepping themselves to have a spell ready in their slot before bed, it automatically means either doing the experiment, or prepping their spell slots. It also would come at material and experience costs.
I would further require a basic outline of the experiment in written form from the player, with a well stated hypothesis, based exclusively on already established information exclusively from that world.
EG, if the player wants to experiment with circumventing the distance cutoff with an area-bound spell with dimension door, he can easily test to see if that is possible or not under controlled circumstances; it will burn the spell use for dimension door, and that spell he wishes to test with. His reasoning may be that other effects are observed that would suggest distance behaves differently through the door (eg, a lightsource near an open dimension door is able to cast strong light at the distant exit of the door, as evidence by somebody looking through one without going through.)
Simple observations about things can be handled with a perception check. (somebody else makes and uses a door-- If the wizard explicitly tries to observe for interesting effects-- like the light stated earlier--- it's just a perception check, but it still gives him knowledge to formulate an experiment with later.)
etc.
What I am saying, is that it can be done in a way that is no more painful for the party than brewing a batch of potions is, or spotting a trap is.