I think I managed 8 turns (nice puzzle btw)
Abbrevations (keeping the alphabetic order):
BO: Border Village
BR: Bridge
CA: Caravan
CH: Chancellor
CR: Council Room
HW: Highway
in addition to these actions I'll use contraband (CO)
The CH is used to discard the draw pile, if no actions are played afterwards
notation:
Turn X:
actions & treasured played
available coins (#buys) cost difference - buys and gains
open CA + CH
Turn 3:
CA, CH + 4x copper
6 (1) 0 - buy BO, gain BR
Turn 4: (draw 1 card from CA)
BO, BR, CH + 4x copper
7 (2) -1 - buy BO, gain BR, buy silver
Turn 5:
2xBO, 2xBR, CA, CH + copper + silver
7 (3) -2 - buy BO, gain BR, buy CO
Turn 6: (draw 1 card from CA)
3xBO, 3xBR, CH + CO + silver
10 (5) -3 - buy 3xBO, gain 3xCR, buy CA
Turn 7:
6xBO, 3xBR, 2xCA, CH, 3xCR + CO + silver + 7x copper
17 (8) -3 - buy BO, gain HW, buy 7xHW
As CH is not played this turn, the top cards of the draw pile are two estates
Turn 8 (draw 2 cards from CA):
7xBO, 3xBR, CH, 3xCR, 8xHW + CO + silver + 7x copper
17 (8) -11 - buy 8x colony
edit: change of abbrevation