Is it okay to 'sandwich' rigid foam insulation between old and new sheet siding?
In theory, that's fine. However, 1/2" is nowhere near enough insulation, and may actually create more problems than it solves, especially if you live in a cold area and your wall studs are deeper than 2x4. Thin foam like what you're proposing can cause wintertime condensation on the inside of whatever's right behind it. I would recommend at least a full inch, and more is better. Obviously this will complicate the trim around windows and doors, but you can easily install jamb extensions to handle that. 4 inches is not overkill, and if the depth is a problem, you could just remove the T1-11 siding first.

Another thing to mention: you have a perfect opportunity to add a radiant barrier, which will make a big difference if you live where it gets hot and sunny. Choose a foil-faced insulation board and face the foil outwards. Then fasten 1" thick vertical furring strips over the foam to create an air gap, and fasten your new siding to the furring strips. It will make a big difference.