Absolutely agree, especially when being used on thin stock.
Pro installers tend to use a compound miter or chop saw as it lets them hold the stock firmly while making the cut.
Is your goal to make them narrower and shorter and reduce the glass area as well? Every storm window I’ve encountered was assembled with cast aluminum corner pieces crimped into a tubular extruded frame. These are not easily disassembled without damage.
I get not wanting to caulk, for sure.
If this were me, I’d seriously consider:
- router the inner edges of the outer wood trim boards to the size of the outer edge of the aluminum window frame. This creates a recessed mounting surface and removes the splintered current mountings. Use a router bit with a guide bearing set properly. (Some manual chiseling to “square” the corners would still be needed)
- then, because the “ledge” is still too narrow, add a ledger strip (use weatherproof glue and nails) to create a more secure (and now weather resistant attachment)
- lastly, maybe, add a bit of aluminum flashing to re-direct rain coming down from the upper trim piece out away from the aluminum frame.