For vault analysis, we need to calculate the number of cards we can have in the deck and the number of cards we need to play in order to draw all of them. So, assume BM in game, YW active, potions active and Colony/Platinum as well. This gives us 246 (38 Victory, 158 Treasure, 10 Curse, 10 BM, 25 BM deck, 5 prizes) cards + 10 Kingdom decks for the game, for 346 cards in game, we must leave at least 19 in supply or game ends, but most of those can be gained on last turn by playing some actions - Ironworks/Uni (if we assume having only KC as above 5$ action or 4$ card, possibly only 6 cards will remain in supply when we play vault - Gold, Platinum, Duchy, Province, Colony, KC). So, we are talking on up to 330 cards deck during last turn (in which we start with 317 in deck), BTW, I'm assuming opponent was inactive, not actually helped by giving his cards as well, can be done using Amb, and can go to 0 cards without trashing by collaborating and using both Amb and Masq. But how do we draw so many cards? The best draw comes from Crossroads for up to 44 cards (33 basic victories+11 from BM deck, Farmland must be bought with no card in hand. Also assuming we have 44 cards in hand, otherwise it's a hand multiplier), then +4 from Council Room/Envoy (Tactician gives 5, but can't be courted). So, start with KC->KC->(CR(12 cards draw, 14 cards hand), Crossroads (for 13,26,44 cards), KC->(IW,IW,KC->(IW,Uni,KC->(Crossroads, Crossroads, Vault)))). This gives a total draw of 365 cards. We played 14 cards and can now discard 315 on the vault for 315$.
I'll try to find how much you can get from Diadem, it will probably not be higher, as you can get only ~220 actions from the TR-KC chain, using Tributes and villages.