Misc,
One thing you can do to create more room for the under cab light is raise the deck up about 3/8" and use it as a door stop as well.
It will need to be edge banded prior to clamping on the frame and should be sized down accordingly.
I am in full on, 100%, with out a doubt agreement with Leo about your finished ends being flush with the frame. (there I said it and I'm still here)
I think you must be stuck on the notion that dadoing the box into the frame is the way to go. If you want to listen to me, let that go as a thing of the past. Not worth the effort and you are not stuck with the modular cabinet look at the finished ends.
We get great results with glue only holding the frame on. In some cases where clamping is not convenient a few pocket screws do the trick if you can hide them.
Have you got a pocket cutter yet? It will change your life to the better.
For the record this is not at all a bad look.