(this is not a hint)
(this is still the old picture and I am too lazy to update it)
I think that the draft is difficult to perform in a single player game. Part of the draft mechanic is that you decide which tiles to deny to the next player; you miss that with solitaire.
Drawing 3 cards and picking one might be interesting. Or you could do 5/4/3/3/2/1 if you wanted numbers more similar to drafts.
You may also need to play without objectives. I could try this out and see how it works.