Dan,

It's clear from your description that you've set up the saw so that the strip comes off between the blade and fence. That seems to be a very popular way to do it, as no fence adjustments need to be made. But in doing it that way, you lose some control over your stock.

If you set up the saw such that the bulk of the plank runs between the blade and fence, the strip will come off easily and fall away as soon as it's separated. The only down side is that the fence needs adjusting for each run of the planks. There's a quick, repeatable way to do it so that you get consistent strips, though they come out even better when planed for consistency. I set up my table saw to do the "planing" too and it all turned out nicely.