I’ve found that no sleeves commonly available seem to work with the stock box insert. I would recommend going to a custom storage solution - several of them reuse the same Dominion center box but replace the insert.
Yeah I've been trying to avoid that (I'm lazy) but it's looking like that might be the best answer.
My lazy storage solution is the Base box with the Base Cards box glued in the middle. This leaves three equally sized compartments which fit Mayday sleeved cards stored horizontally
perfectly. If you don't have it you could just make three rows and slide in two cut out sides of a Dominion box (or just any pieces of cardboard I suppose) in between; since the fit is so good they shouldn't slide around. This doesn't require any materials you don't already have, is quick to make and it's kind of nice to have your Dominion cards in the Dominion box. You will need dividers, I made mine with
this website.
My box holds Base, Intrigue, Seaside, Adventures, Empires and all the mats and tokens. There's enough room to fit in Nocturne if I store the tokens separately (although the mats still fit if I put them on top of the cards). If you have all the sets, you can probably fit all the cards in a large box and a small (Alchemy etc.) box, you can certainly fit everything in two large boxes with plenty of room to spare. One Dominion box is a small enough to be transported in a regular backpack in my experience. I am very pleased with my 0$ storage solution.