Not a teacher, but maybe you can investigate a little and find a unit that does their 2 weeks during the summer (mine does).
As a reservist you go in KNOWING your unit, and commanders before you even go to Basic. Also, I essentially know my drill schedule 12 months ahead of time.
So all you would have to do is find the units you are interested and ask to see their drill schedule.
Also, as a reservist you have some latitude in when you can make up any missed drill days. In fact my unit apparently is pretty crazy and has two separate 2 week training stints. We don’t have to go to both of them (in fact they really don’t allow us because of costs).
So if you want it bad enough I don’t see what would conflict with your teaching job (outside of a deployment).
My biggest pain was getting time off work to go through MEPS and take all the testing and jumping through hoops. If you have time now DO IT while you can in the summer ASAP.