You really think that, say, the pharma industry's lobbyists are going to invest resources in opposing, say, reform of gerrymandering, or of alternative voting systems?
I'd say it's a LOT more likely that the obstacle is the politicians themselves, because the emergent behavior of the status quo is that it insulates incumbents from competition.
A successful 'trial' (one might even be able to convince them by saying it's going to be a trial at first) might convince other state politicians and/or people elsewhere to implement similar systems in their own state.
Disclaimer: I am Danish and Denmark apparently ranks top in their PEI index.
Joking aside...
understand that we don't actually have a national election system, or even a state one. Each one of the United States 3,142 counties runs an mostly independent election managed by an elected county election commissioner. Tallies for higher elections are reported upward from there. In some states there may be some unification as far as selecting common voting hardware across the state but in most places, even that is at the discretion of the county. So, to your original question, The federal government simply does not have the power to choose a "minor" state to run a trial in.