Here's my solution.
A high level description:
We'll base the overall solution on the solutions to the predecessor puzzle (gain all Treasures by turn 5). Key cards for setting up an engine quickly: Ironworks, Chancellor, Throne Room, King's Court, Watchtower, Bridge, Council Room.
Our main way to get cards, though, will be Haggler instead of Talisman. Since we can't Haggle for Victory cards, the hardest part will be buying green. We will buy green, and Haggle off of it.
We use Border Village instead of Duchy, so that we can Bridge 5 times, rather than 4.
We use the Black Market deck to introduce cards for helping us gain Estates, which we can't Haggle anything off of. We use Workshop and Baron (which also gives precious buys!). We use Young Witch in the deck to introduce an 11th Kingdom card.
Upgrade is this last Kingdom card. It's useful for getting the engine going at the start of the 5th turn, by getting us 4 costs and drawing.
Here is the solution, in full detail. I double checked, but there are still probably mistakes, so please let me know!
C = Copper
E = Estate
B = Bridge
H = Haggler
I = Ironworks
K = King's Court
M = Black Market (Contains Young Witch, A = Baron, O = Workshop, Z = Goons)
N = Chancellor
U = Upgrade
R = Council Room
T = Throne Room
V = Border Village
W = Watchtower (bane)
===
Turn 1
===
Draw CCCCE
Play CCCC
Buy I
===
Turn 2
===
Draw CCCEE
Play CCC
Buy N
===
Turn 3
===
Draw CCCIN
Play I for T
Play N, discarding
Play 3 C, buy W
===
Turn 4
===
Draw ITNWC
Play T on I, for T and I, top-decking both
Play W, drawing TICC
Play I, for B.
Play T on N, discarding.
Play CCC, buy K
===
Turn 5
===
Draw TKBIW.
** Play:
** Hand: TKBIW
** Deck: NTI CCCCCCCEEE
Play T on K.
-1st K plays B
-2nd K plays I for KKR, revealing W and putting all on top.
Play W, drawing KKRNTI
** Play: T K B I W
** Hand: KKR NTI
** Deck: CCCCCCCEEE
Play T on K.
-1st K plays I, for KUU
-2nd K plays K
** Play: TT KKK B II W
** Hand: N R
** Deck: CCCCCCCEEE KUU
--1st K plays R, drawing CCCCCCCEEE KU
--2nd K plays U, turning EEE into TII, drawing UTI
--3rd K plays K
** Play: TT KKKK B II W R U
** Hand: N CCCCCCC UTI
** Deck: I
---1st K plays I, for KKR
---2nd K plays U, turning CCC into IIB, drawing IKR
---3rd K plays K
** Play: TT KKKKK B III W R UU
** Hand: N CCCC TIR
** Deck: KIIB
----1st K plays I, for KRU
----2nd K plays T
-----1st T plays R, drawing KKIIBRU
-----3rd T plays U, turning CC into II, drawing I
-----2nd T plays B
----3rd K plays K
** Play: TTT KKKKKK BB IIII W RR UUU
** Hand: N CC III KR
** Deck: I
-----1st K plays I, for KKK
-----2nd K plays I, for RII
-----3rd K plays K
** Play: TTT KKKKKKK BB IIIIII W RR UUU
** Hand: N CC I R
** Deck: IKKKRII
------1st K plays I, for MTH
------2nd K plays R, drawing KKK R III MTH
------3rd K plays K
** Play: TTT KKKKKKKK BB IIIIIII W RRR UUU
** Hand: N CC KK R III MTH
** Deck:
-------1st K plays I, for HHH
-------2nd K plays I, for HHH
-------3rd K plays K
** Play: TTT KKKKKKKKK BB IIIIIIIII W RRR UUU
** Hand: N CC K R I MTH
** Deck: HHHHHH
--------1st K plays M, gaining A, O, and Z
--------2nd K plays I gaining HHH
--------3rd K plays K
** Play: TTT KKKKKKKKKK BB IIIIIIIIII W RRR UUU M
** Hand: N CC R TH
** Deck: HHHHHH AOZ HHH
---------1st K plays R, drawing AOZHHHHHHHHH
---------2nd K plays A, gaining EEE
---------3rd K plays O, gaining EEE
** Play: TTT KKKKKKKKKK BB IIIIIIIIII W RRRR UUU M A O
** Hand: N CC TZ HHHHHHHHHH
** Deck: EEEEEE
Play T on Z. Play N. Play HHHHHHHHHH. Play CC.
We've played 5 Bridges, 3 Barons (not discarding), 2 Goons (same card), 11 Council Rooms, 10 Hagglers, 3 Black Markets, a Chancellor, and 2 Coppers. We also lost $1 for buying Goons.
This gives us $38, 22 buys, everything costs 5 less, and we have 10 Hagglers in play.
The piles counts are:
8 Provinces
8 Duchies
2 Estates
30 Golds
40 Silvers
53 Coppers
10 Curses
0 Hagglers
0 Ironworks
0 King's Courts
10 Border Villages
8 Bridges
9 Black Markets
9 Chancellors
7 Upgrades
6 Council Rooms
7 Throne Rooms
9 Watchtowers
= 55 non-Border Village Kingdom Cards
Buy 8 Provinces, Haggling to gain 26 Gold, 53 Coppers and a Curse.
Buy 4 Golds, Haggling to gain 40 Silvers.
Buy 10 Border Villages, gaining 8 Duchies and 2 Estates, and Haggling to gain the other 55 Kingdom Cards (King's Court is gone), 9 Curses.
I may be able to also get Platinum and Colony. Will work on this in the next few days, maybe. We'd probably want 7 Bridges played, some more money, and just a tad more buys. In this version, I had 3 extra buys and some leftover money.