If you drop some presumptions about the players you can go even faster-- Player 1: Roll a 3, 5, 6, 8, 9, 11 or 12. Don't purchase, so it goes to auction. In auction player 2 buys for 100% of their cash. Player 2: Rolls a 4, lands on income tax. Game over.
Of course it ignores the auction rule, but it could be amended to say the loser buys each auctioned property for a dollar (or whatever amount.) The only decisions the loser makes in this case are their bid prices which are irrelevant. The outcome is the same.
Edit: Actually it's a bit more complicated than this, as buying all of the auctioned properties and mortgaging them would give Player 2 enough money to afford the rent on Boardwalk. Player 1 would have to bid close to the mortgage price for each property. That way if they win the auction they can mortgage it to get their money back to afford houses, and if they lose the auction it doesn't help Player 2 afford rent on Boardwalk.