I don't see a sled in the original post. According to the original picture I'd have the thicker piece of wood between the blade and the fenceActually, you don't use a push stick. You slide the whole sled forward. It allows you to keep a hand to each side and out of the blade.
I find that running a board through the table saw leaves the cut edge straighter than the opposite edge. So if the "waviness" is not too bad, I run the board through with the straighter edge against the fence, and cut a "better" edge on the opposite side. Then turn the board around and put the "better" edge against the fence, and cut an "even better" edge. Maybe have to turn the board around one more time and put the "even better" edge" against the fence.....How can you make a straight edge on wood that has no straight edges to begin with?