My solution is coming up with a KC-Bridge mega turn.
Kingdom: King's Court (KC), Bridge (Br), Fool's Gold (FG), Chapel (Ch), Mint (M), Governor (Gov), Moat, Chancellor, Baker, Fortress (F) --> With Colony
Turn 1: CCCCC --> M
Turn 2: CCEEE --> Ch (Deck is CCEEE M Ch)
Turn 3: CCEEE --> FG (Note: I am not sure if "worst luck" is $1 or $2 here. If you have $2 you have to buy the FG, and then trash 3 junk turn 4. If you have $1 you have to not buy the FG, and then trash 3 junk turn 4 (keeping a Copper) and spending the coin token. Either way, you will get a 5 card deck for Turn 5 - A chapel, a FG, and 3 junk cards. I am about 98% sure you will regardless be able to get down to Ch + FG + FG (and maybe a copper) for turn 6, however.)
Turn 4: M + Ch + CCFG --> Trash M, C, C, Buy nothing
Turn 5: EEE + Ch + FG --> Trash EEE, Use Coin Token, Buy FG
Turn 6: Ch + FG + FG --> Buy Br
Turn 7: Ch + FG + FG + Br --> Buy KC
Turn 8: KC + Br + FG + FG + Ch --> KC-Br, Buy KC + Br + Gov + Gov
Deck is now: 2x KC, 2x Br, 2x Gov, 2x FG, Ch
In turn 9, you MUST have a Gov or enough money to buy a Br.
If you do not have a Gov, you MUST start turn 10 with 2 Gov, and using them for draw, you can draw your whole deck and play KC-KC-Br-Br-Br and win.
If you do have a Gov, use it for cards. You MUST have at least 1 KC and at least 1 Br. You MUST have at least 2 of: KC, Br, Gov.
If it is KC and Br, you can play KC-KC-Br-Br-Ch (trashing 2 FG). Buy a Br. You have a Gov on top of your deck, use it for draw, play KC-KC-Br-Br-Br and win.
If it is KC and Gov, you play KC-KC-Gov (trash Ch for Fortress) (trash FG for Fortress) (trash FG for Fortress)-Br, and buy a bridge. Turn 10 you will have all self replacing cards until you can play KC-KC-Br-Br-Br and win.
If it is Br and Gov, you can play KC-Gov (trash Ch for Fortress) (trash FG for Fortress) (trash FG for Br), and buy nothing. Turn 10 will have all self replacing cards until you can play KC-KC-Br-Br-Br and win.