I forget how the "control" is handled over these things. I think before the game starts, its largely up to the home team but with feedback from MLB as to how to proceed. And then once the game starts, its the umpires (ie, MLB) along with feedback from the home team.
I think the next reasonable day off is Thurs April 25. The Tigers are going from a Tampa 7pm game on Weds to a home 1pm game on Friday, so definitely not ideal there. The Mets have a 3pm (EDT) game in San Francisco on Weds and return home for a 7pm game on Fri. I suppose MLB could force the Tampa start time to earlier, but I don't know if Tampa could push back.
Whatever happened to MLB pushing clubs for day time starts for getaway games? Maybe that doesn't apply when the next day is an off day.