It's time.
My solution is probably not perfect. I don't know if I formatted it in a way that's easy to follow. With apologies out of the way:
In a solitaire game of Adventures, with only 2 events, we can empty the supply in 8 turns.
The Kingdom:
Artificer (A)
Bridge Troll (B)
Coin of the Realm (Cotr)
Magpie (Mag)
Messenger (Mess)
Miser (Mis)
Royal Carriage (R)
Storyteller (S)
Treasure Trove (T)
The last one doesn't matter. My solution only involves the first nine.
Copper is abbreviated as C; Estate as E.
The Events around which everything hinges:
Traveling Fair
Inheritance
The solution itself:
Turn 1: CCCCE. Buy Mess, gain Mag with it.
Turn 2: CCCEE. Buy Cotr.
Turn 3: MessMagCCCotr. Play Mag, draw E and reveal E. Gain a Mag.
Play Mess, discard deck. Play treasure and put Cotr on the tavern mat. Buy B and C.
Turn 4: MessBMagMagC. Play both Mags, draw CCCC. Play B, call Cotr, Play Mess and discard deck.
We have $7, 3 buys, and cost reduction. Buy Inheritance and choose Royal Carriage. Buy CC.
Turn 5: EEEMagMess. Play Mag1, draw Mag2 and reveal C. Play Mag2, draw C and reveal Cotr.
Hand is EEEMessCCCotr. Play all E as R. Play Mess and call E 3 times. Discard deck.
We have $11, 6 buys, and cost reduction. Buy Mess and gain B. Buy B. Buy 4xE.
Our deck is now: 10xC, 7xE, 2xMag, 2xMess, 3xB, Cotr (on mat)
Turn 6: 4xEMag. Play all 4xE. Play Mag, call all E. The deck is: MagMessEEEB.
We draw MagMessEEE, and gain 5xMag. Play Mess and discard deck.
Play 3xE. Play Mag and call 3E for four Mag plays. We draw 4xMag, and reveal 4xC.
Play another Mag, draw Mag#7 (the last one) and reveal C.
Play all 4 remaining Mag, drawing BBBMess and revealing 4xC.
Our hand is 3xB, Mess, 9xC. Play all actions, discard remainder of deck.
We have $13, 6 buys, and cost reduction x3. Buy last 4xE in supply. Buy Mess, gain B.
$12 and 1 buy remain. Buy Travelling Fair 3 times: $6 and 4 buys. Buy RRACotr.
Our deck: 11xE, 10xC, 3xMess, 7xMag, 5xB (3 are in play), 2xCotr (1 on mat), 2xR, A.
Turn 7: BBMagMagMag. Top of deck has ACotrEEE. Play BB, call Cotr, Play 3xMag. Draw A, reveal Cotr, draw EE, gain 2xMag.
Play EE. Play A and call EE.
For the next part, we will be numbering the cards so as not to lose track.
Draw E, gain and draw A#2 and R#3, gain R#4.
Play E and R#3. Play A#2 and call on it. Draw R#4, gain and draw A#3 and R#5, gain R#6.
A#3, call R4 and R5 on it, draw R6, gain/draw A4 R7, gain R8.
A4, call R6 and R7 on it, draw R8, gain/draw R9 (the last one due to Inheritance) and A5. Gain A6.
Note that at this point, our hand is Cotr, R8, R9, A5. We’ve made 12 coins via artificer.
A5, call R8/R9. Draw A6, draw/gain A7 A8, gain S. 15 coins.
Play A7, draw S gain T. Play A8, draw T gain A9. 17 coins.
Play Storyteller, targeting Cotr and T. Spend a total of 21 coins. Draw 21 cards.
Put Cotr on mat, gain C and G.
Our deck (not yet played) includes 3xMess, 8xE, 11C, R1 and R2, A9, 6xMag, G.
We draw 8xE, R1, R2, A9, 6xMag, 3xMess, G. Remaining deck is 11C.
Play R1, R2, and 8xE. Play A9 and call it 8 times. Each time, gain Miser.
We draw C and 8 Misers, Leaving 1 Miser on deck.
Play Magpie. Draw Miser, reveal C.
Remaining Magpies draw remaining C.
Our hand is now 9xMiser, 11xC, G, 3xMess, and 2 Royal Carriages on mat.
Play Misers and call remaining Rs on them to put 11 C on the mat.
Play 3xMess and G. We have $9 from the last Artificer.
$18 and 9 buys. Buy Travelling Fair 9 times for 18 buys.
Buy Mess (gain S), 6xCotr, 6xT, 5xS
Current deck: 11xC (on mat), 8 Cotr (1 on mat), 7xT, 7xS, 5xB (2 in play), 9xMis, 4xMess, 9xMag,
11xE, 9xR, 9xA, G.
Turn 8: Start with 5xMag. Draw 4xMag and S, revealing Mag (to gain last Mag) 2xCotr, and 2xT.
Play 4xMag to draw 3xB and S. Reveal 5xT. Current hand is 7xT, 2xCotr, 2xS, and 3xB.
Play S on CotrCotrT. Gain GC, put 2xCotr on mat, draw SMess 3xA.
Play S on 3xT. Gain 3xG, 3xC, draw S 6xA. Hand: 2xS, 3xT, 9xA, Mess, 3xB.
Play S on 3xT. Gain 3xG, 3xC, draw 7xE. Hand: S, 9xA, Mess, 3xB, 7xE.
Play 3xB and call 2Cotr (1 left on mat). We have 2 actions.
Play A. Draw S, gain A. Play A, Draw A, gain T. Continue to play 8xA, drawing T, gaining AND drawing T, 2xB, 2xCotr, 2xS. Gain, but do NOT draw Miser.
Hand is 2xT, 2xB, 2xCotr, 4xS, Mess, 7xE.
Play Mess, discard deck. Play S on TTCotr. Gain 2xC, 2xG, and draw (10+2+6) 19 cards.
So far, we have played 4xS, 9xT, 10xA, 9xMag, 3xB, 3xCotr (2 called, 2 on mat), Mess.
Remaining deck contains 9xC, 10xG, 4xE, 9xR, 10xMis, 3xMes, 2xB, Mag, 1xS, 6xCotr.
We draw: S, 5xCotr, Mag, 10xG, E. Hand is 5xS, 6xCotr, Mag, BB, 8xE, 10xG.
Remaining deck is 9xC, 3xE, 3xMess, 10xMis, 9xR.
Play Mag, draw E reveal C.
Play S on 3xCotr, draw 4C.
Play S on 3xCotr, draw 4C.
Play S on 3xG, draw EE 8xR
Play S on 3xG, draw R 9xMis
Play S on G, draw Mis 3xMess.
Our hand is now 9xC, 3xG, 2xB, 11xE, 9xR, 10xMis, 3xMess. There are 8 Cotr on the mat.
Play 9xMiser, putting 9xC on the mat. Call 5 Cotr for actions. We should have 2 actions now.
Play all E and R. Play last Miser and call them for 21 effective Miser plays. Choose coins.
With 20C on the tavern mat, this equates to $420.
Play 2xB and 3xMess, calling Cotr as needed. We have enough.
On our final buy phase, we have (420+6+9) $435. We have (7+4+1) 12 buys.
There are 7 Bridge Trolls in play.
Purchase Travelling Fair 213 times, leaving $9 for provinces.
Provinces cost 1, and everything else is free. We have 225 buys. Empty the Supply!
Edit: Literally right after I post this, I think "I wonder what would've happened if I'd done X instead" and accidentally come up with another solution that might be 1 turn faster. Oh well. At least I wrote up SOMETHING.