Ken, for making small, flat adjustments to small objects, another quick and easy option is a benchtop belt & disk sander. They have guides to keep your piece square and with gentle pressure, you can be super accurate.

You can pick up benchtop sander for a hundred bucks on sale and feel like you have gotten your money back in no time at all. Also, it's one of the very few power tools where a decent but relatively inexpensive one, works as good as an expensive one. The one thing to look out for is some "super cheap" ones are hard to set up and keep the guides square.

Mark, not having a proper M&T jig, I probably would have fashioned a jig out pf scrap wood to support and slide the piece as I ripped it across the tablesaw, as suggested. Essentially, it would have fit inside your "J" shape turning it into a solid block again. Add cap pieces at the ends to keep it from popping out during cutting. Also, by having it a solid piece with caps at the end, there is no place for tear out.

Always lots of ideas for any problem eh? That's one of the things I like about woodworking. The problem solving.
With great power comes Awesome irresponsibility.