Two other options:
A) Clamp a batten to the work to guide the saw
B) Don’t saw. Instead, cut this entirely with chisel and router, like a housing.
On the existing shooting board, if your wedges stay in and are at the right angle, you can use the shooting board. If things are a little sloppy so that the wedge does not stay, you can knife a new line and clean to it with the chisel. This will widen the wedge housing, but that’s okay- just seat the wedge further and trim it shorter as needed. You probably don’t need to start from scratch on this!