Stacks: r1 y5 b5
Alice: b1 b2 b3 b4
Bobby: r1 r1 y1 r2
Carol: y2 y3 g4 g4
David: r3 w3 w3 g5 
Wins: 2
Deck: r4 r5 .. g1 g2 g3 .. kt w4 w1 w2 kt .. w5
Line: dc r2 .. r3 r4 r5 .. g1 g2 g3 g4 g5 .. w1 w2 w3 w4 w5
Plan: P  Y  R  O  P  H  O  R  I  C  R  O  O  F  T  O  P  S
Display: Pyrophoric rooftops

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[P] Turn  1 ..... Alice discards a stale card and draws [P] red 4
[Y] Turn  2 ..... Bobby plays [F] red 2 and draws [U] red 5
[R] Turn  3 ..... Carol stalls by spending a clue
[O] Turn  4 ..... David plays [K] red 3 and draws [C] green 1
[P] Turn  5 ..... Alice plays [P] red 4 and draws [H] green 2
[H] Turn  6 ..... Bobby plays [U] red 5 and draws [M] green 3
[O] Turn  7 ..... Carol stalls by spending a clue
[R] Turn  8 ..... David plays [C] green 1 and draws any card
[I] Turn  9 ..... Alice plays [H] green 2 and draws [T] white 4
[C] Turn 10 ..... Bobby plays [M] green 3 and draws [E] white 1
[R] Turn 11 ..... Carol plays [R] green 4 and draws [J] white 2
[O] Turn 12 ..... David plays [W] green 5 and draws any card
[O] Turn 13 ..... Alice stalls by spending a clue
[F] Turn 14 ..... Bobby plays [E] white 1 and draws [Y] white 5
[T] Turn 15 ..... Carol plays [J] white 2 on their last turn
[O] Turn 16 ..... David plays [O] white 3 on their last turn
[P] Turn 17 ..... Alice plays [T] white 4 on their last turn
[S] Turn 18 ..... Bobby plays [Y] white 5 on their last turn

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PROOF OF UNIQUENESS

Despite the long length of this sub-puzzle,
it is actually fairly straightforward compared
to the preceding two sub-puzzles,
because it is more constrained.

The starting pace is +1,
so at most one discard is possible.
However, Alice has no cards to begin, so she must discard,
and thereafter no more discards are possible.
However, Carol has no plays to begin, so she must be given clues
until her green 4 is playable.

On the first round, Bobby should play r2 (his only playable card),
Carol uses a clue, and then David can play r3 (his only playable card).

At this point, there are only two plays now
(Alice and Bobby's drawn cards),
so it is not possible to get Carol's g4 to play.
Thus the team needs to generate a clue for Carol.
This can only happen if Alice plays r4 and Bobby plays r5,
giving Carol a clue to spend.

This gives the players another three turns to either reach a 5
or give Carol a play.
Since both the green and white stacks are empty,
the former is impossible,
but the latter is possible in exactly one way:
David plays g1, Alice plays g2, Bobby plays g3,
letting Carol play g4.

At this point, David cannot be the one to play (or draw) w1,
because David holds both w3's --- meaning that if David plays w1,
only one of Alice, Bobby, Carol would have a play on the next three turns,
causing the players to lose since the pace is zero and no clues remain.
Therefore, David should play g5.

Now the only cards to play are the white cards.
David holds both w3's, so among Alice, Bobby, Carol,
two of them play w1 and w2 and one of them should burn a clue.
However, there is only one card remaining,
so whoever plays w1 will trigger the final round.
If Alice triggers the final round, there is not enough time
after David's turn to play w4 and w5, so Alice must spend a clue,
and let Bobby and Carol play w1 and w2.
Then David plays w3, Alice plays w4, and Bobby plays w5.

Looking at the deck order,
all the cards are constrained except for two unused cards,
namely David's last two draws.
These two unused cards can come in either order,
so 2 of the deck orders lead to wins.