What is the best strategy for the solitaire game Golf?

Question

In Golf, 35 cards are dealt into seven face-up tableaux of five cards each, all of which are visible at once. Then one card is dealt face-up to form the discard pile, and the remaining 16 cards are put in a face-down stack ("the stack").

On each turn, the player places a card face-up on top of the discard pile subject to the following rules, listed in decreasing order of precedence. Call the topmost discard the "active card."

1. The top card of the stack may be discarded to form a new active card, regardless of the rank of the current active card.
2. No card may be discarded onto a King.
3. Only a 2 may be discarded onto an Ace.
4. A discard must be adjacent in rank to the active card. For example, if the active card is a 7, then only a 6 or an 8 may be discarded.

The object of the game is to discard all 52 cards.

What is the best strategy for this game, and what per cent of games are winnable with perfect strategy?