SplinterGroup .... I've also seem "small parts" jigs where the cutting platform is raised a small amount on the cutoff side of the blade.
Set your stop, move the stock over to the stop and hold it down, release the stop and cut (like you have it). Except now the cutoff is riding on the raised platform (< 1/2 the width of the cutoff) and it tops off the platform and away from the blade.
A "jam free" (maybe vegemite) stop-block is only required for really small pieces when there is insufficient space for a few fingers each side of the blade. I did think of cannibalising a small light safety pin, as a standard spring compression/expansion would became too bulky and there was a limit to over engineering. Normally I would use that small rubber on a narrow dowel (can imagine SWMBO cackling in the background) to hold it down, but no matter how well I plan, it's always on the other side of this lazy ducks workshop.
Not sure I can accurately picture your raised platform setup... someone needs to learn SketchUp.
If your first cut is too short... Take the second cut from the longer end... LBD