Masq is cheating.
Mostly because it had slipped my mind of course.
I've found a couple of solutions with 3 players without Masq's voluntarily Province passing.
Baker is in the kingdom, giving every player a Coin.
Turn 1
P1:
- Open Noble Brigand
-- Flip P2's E+C
-- Flip P3's 2E, giving him a C
P2:
- Open Council Room
-- draw EEC, reshuffle, draws CR + 1 more card
P3:
- Open Tournament with 4C-E
-- draw CCC, reshuffle, draws T + C (4C, 3E left in draw deck)
Turn 2
P1:
- Use Coin to buy NB
-- Flip P3's 2E, giving him a Copper (P3 has 4C, 1E left in draw deck)
P2:
- Play Council Room
-- Draw 4 cards
-- Make P3 draw a Copper (P3 has 3C, 1E left in draw deck)
-- Buy Noble Brigand
--- Flip P3's C+E (P3 has 2C left in draw deck)
P3: Has 5C + T in hand
- Play T, draw C, use Coin to buy Province
-- Draw C, reshuffle, draw Tournament + Province + 2 extra cards
Turn 3
P3: Play Tournament, reveal Province, gain Prize
Alternate solution, uses Shelters: (S) or (OE/H/N):
Turn 1
P1:
- Open Noble Brigand
-- Flip P2's H+C
-- Flip P3's 2C
P2:
- Open Council Room
-- draw SSC, reshuffle, draw CR + 1 more card (6 cards left in draw deck)
P3:
- Open Stonemason + Tournament/Death Cart/2 Ruins with $5 + Coin
-- draw OE+H+N, reshuffle, draw T + DC (7C, 2R, SM left in draw deck)
Turn 2
P1:
- Use Coin to buy NB
-- Flip P2's whatever
-- Flip P3's 2R, giving him a Copper (P3 has 7C, SM left in draw deck)
P2:
- Play Council Room
-- Draw 4 cards
-- Make P3 draw SM (P3 has 7C, left in draw deck)
-- Buy Noble Brigand
--- Flip P3's 2C (P3 has 5C left in draw deck)
P3: Has OE+H+N+T+DC+SM in hand
- Play N
- Play SM, trash OE, draw C (gain 2C)
- Play T, draw C (3C left in draw deck)
- Play DC, trashing it
- Buy Province with 2C, $1 from T and $5 from DC, trash H
- Draw 3C, T+P
Turn 3
P3: Play Tournament, reveal Province, gain Prize
You can have some fun with the alternate solution and shuffle some things around, like having P2 buy 2 Noble Brigands on T2 to flip some more cards, but the basic ingredients for my solutions are:
- Noble Brigand flipping
- Council Room (perhaps Governor) drawing
- Stonemason/Tournament/Death Cart or plain Tournament with Coppers
Maybe Stonemason/Tournament/Envoy works or something similar like SM/Tourney/Coppersmith.