So the only events we are actually using are Alms, Borrow, Quest, Save, Scouting Party, Travelling Fair, Bonfire, Expedition, Pilgrimage, Ball, Raid, Trade, since the rest depend on Action cards.
I figure the standouts are Raid(gain loads of Silver), Scouting Party(for shuffle control), Travelling Fair(for buys), and Borrow/Save to distribute money between turns. Saw the Quest thing, but I don't think buying Curses is worth it, and obv discarding 6 isn't either.
T1: Buy Scouting Party(discard 3 Estates) + Silver, shuffle and draw 5 copper
T2: Buy Scouting Party(discard 3 Estates) + Silver, draw Silver, 2 Copper, shuffle, Silver, Estate
T3: Buy Borrow, Scouting Party(discard 2 Estates and Copper), Raid(gaining 2 Silver), draw 4 Copper
T4: Buy Expedition, shuffle and draw 4 Silver, 3 Copper
T5: Buy Travelling Fair, Raid(gaining 4 Silver topdecked), Borrow, Raid(gaining 4 Silver topdecked), draw 4 Silver
T6: Buy Province, draw 4 Silver, Copper
T7: Buy Scouting Party(discard 3 Estates), Scouting Party(shuffle, discard 3 Copper), Expedition, draw 7 Silver
T8: Buy Travelling Fair, Raid(gaining 7 Silver topdecked), Raid(gaining 7 Silver topdecked), draw 5 Silver(top of deck has 9 new+5 old=14 Silver)
T9: Buy Borrow, Save(Silver ofc), Province
T10-12: Repeat 3 times. Draw 2 Silver, 2 Copper, saved Silver
T13: Buy Province(number 6), draw 5 Copper
T14: Scouting Party(discarding 3 Estates), Expedition, draw Province, shuffle and draw 6 Silver
T15: Buy Province, draw 4 Silver
T16: Buy Province
Definitely room for improvement here. I was thinking that if you could buy Travelling Fair+Expedition, you could increase your hand size to ridiculous amounts, then Ball for ridiculous amounts of Silver. But then I realized we're capped at 40 Silver, so I just bought out Provinces. You need 2 Expeditions to double Province, along with 9 Silver, so the setup isn't really worth it when you could just buy Province twice.
Keep in mind for fastest BM that 17 turns is normally 2 player, where you only need to get 4 Provinces. Did a bit of simulation, looks like solo standard BM with Duchy/Estate removed takes about 25 turns.
I guess if it's 2 player, then just follow the above and it finishes by turn 11.