Madman + Expedition
Increase your starting handsize so that your Madman draws more cards. Plus, because Expedition isn't a card, you can buy it and get a Madman on the same turn.
I was thinking about what the best supporting card was for the Hermit + Market Square combo. I realized that, by buying Expedition on the turn before the megaturn, one only needs to play two Madmen to fully draw a deck of 24 cards (instead of the usual three). This saves about two turns in the best case scenario. Best-case solitaire log:
1: CCCEE - Buy Hermit
2: CCCCE - Buy Hermit
3: _HCCCE - Trash Estate, Gain Hermit, Buy Market Square
4: HCCCE - Gain Market Square, Buy Market Square
5: EC_HCC - Gain Hermit, Buy Market Square
6: SSHCCCC - Gain Market Square, Buy Expedition, Gain Madman
7: SHE_MCCCE - Gain Market Square, Gain Madman
8: SSSHC - Gain Hermit, Gain Madman
9: SHCCC - Gain Hermit, Buy Expedition, Gain Madman
10: _MMMMHHS - Megaturn with 6x Market Square (45 coins)
Madman + Mission is also worth mentioning. You can gain a Madman on the turn you buy mission and the mission turn itself. In practice, it's unlikely to get 4 coins every other turn in a Hermit + Market Square combo. It is theoretically possible to reach the megaturn on turn 9, though.
1: CCCEE - Buy Hermit
2: CCCCE - Buy Hermit
3: _HCCCE - Trash Estate, Gain Hermit, Buy Market Square
4: HCCCE - Gain Market Square, Buy Market Square
5: EC_HCC - Gain Hermit, Buy Market Square
6: SHCCCC - Gain Hermit, Buy Mission, Gain Madman
*: SSHEE_H - Gain Hermit, Gain Madman
7: SSHCCCC - Gain Market Square, Buy Mission, Gain Madman
*: MHCCC - Gain Market Square, Gain Madman
8: _SSHCCCC - Gain Hermit, Buy Mission, Gain Madman
*: SSHEECC - Gain Hermit, Gain Madman
9: MMMSC - Megaturn with 6x Market Square (48 coins)