You need to build guides to hold the wood against the table and fence with just enough play to allow feed...
A couple straight boards and some clamps might do the trick.
Use a longer straight board against your short fence to extend it as well. The melamine boards work well for that.
Go longer than you need if possible on your cut piece, and you can sacrifice the start/stop ends if they're a little wonky.
[ETA] added (and corrected) melamine. Had guns on the brain when I said melonite. lolz