Right now, the sliders indicate the word BAA. If you move the sliders down far enough, you can indicate the word WRY.
So here's the game: how many words can you form by moving sliders downward? The game is over when the sliders finally indicate WRY.
Note, on each play, exactly one slider moves down.
(For the answer I found using a computer, scroll down.)
HAW (fruit of a hawthorn)
This solution leaves the central A in place for a very long time, eventually harvesting a run of six -AY words before finally taking advantage of the possibilities afforded by the initial letter S to branch out at the middle position.
Here's what the endgame looks like as a graph. Each vertex is a word, and an arrow points from one vertex to another if it is a fair play to change the first word into the second. (I removed direct shortcuts from the graph.) Sorry the word labels aren't visible—LAX is at the top, and TRY is at the bottom.