Doors – Should I sand the frame or buy a custom storm door for an opening that’s 1/8″ too short

You dont state what your problem is. You can install the door to the outside of the door frame. It looks like the top sticks out farther than the sides so you either have to add a board the thickness of the distance to the outside of the side frame. If you need more room for the frame flange at the top you can add a 1x2 board to the top of the door . With the thick door frame the bottom of the screen door may not hit something so you will have to look at that.

Installing a screen door is not an easy project even on a standard door. Especially the first time so if you're doubting yourself you might want to hire someone.

Your idea about the 1X6 on either side is a good start. It would give you something to fasten to, in a simple fashion on both sides, although the fastening would be minimal. You may need to increase the number of nails in the jamb to keep it in place over the long haul. Same thing if you use screws.

When the 1x6, for a 6" wall, or if it fits, 1X8 for an 8" wall, is set in place, use construction adhesive between the block and 1X and let it harden. Make sure your block are clean so the glue sticks. This will give a firm base to work to. Do not skimp on the glue. Use a 10 oz tube, a half tube at least, on each side before you set the 1X. Use concrete screws to fasten it in place, they are more reliable for a first time installer. You could use masonry nails but there are places they may not hold. The screws may fail in their holding, but that will be obvious. To increase the chances of holding, use the screws only in the block, not the joints. Keep the screws about an 1 1/4" to 1 1/2 from the edges of the block. The block is thicker there and is far enough from the edge to keep from cracking out (should be). Screws also only affect a small area when they fail, nails break out larger pieces.

To answer the other part of your question, yes you could use framing only on one side, them shimming and fastening the other side is tricky. There are case hardened finish nails to do this, or even screws. For a first timer, what I mention above should do what you need.