Rather than a full Connections Academy, as I suggested in Idea #2, why not start gradually introducing online classes to the district? In other words, offer some classes in online form, and enable students from any district school to enroll in them, for the same types of credits as standard classes. They can attend online from the local school library or their own homes.
Why would this save the district money? Well, the Oregon Connections Academy has shown that online instruction can handle much larger ratios, up to 50-1. This isn't a surprise to me: much of a typical teacher's energy is taken up by classroom management. Without that issue, they are able to concentrate on the teaching itself. So by offering some proportion of its classes in online form, the district can gradually increase capacity without needing to hire additional teachers.
There are further benefits to this idea as well. If an elective class is rarely offered at any individual school due to low demand, it might be possible to offer it district-wide in online form if there is enough collective demand. And similarly, if an upper-level class is lightly attended at each school, perhaps the classes can be consolidated online, freeing up some teaching resources for other purposes. This could help improve the student/teacher ratio in the more popular 'live' classes.
And, there is the additional benefit that some students who may struggle in standard classes are especially suited for this form of education. In particular, online communication has sometimes been found to be very helpful for people with autistic spectrum disorders.
Some Oregon districts have already been taking steps in this area. This is one trend that I believe we should fully embrace, both for the cost savings and the potential educational benefits.