FWIW @ OP, the schools we looked at all offered courses beyond linear algebra. There are also opportunities to work with math faculty theoretical topics. You will be happy to know that there are many other students like yourself with a keen interest and talent in math. Seriously, you will not bored and you will be challenged by the rigorous math offerings at the schools on your short list.
That being said…there are MANY “repeats” at NE boarding schools. This was a surprise to us. The reasons for this are varied. If you have a inner hunch that you should repeat a grade, then listen to it and decide accordingly. It’s more common than you think and it’s a wonderful opportunity for you. Do not worry about being bored. Many students have already taken classes and are repeating classes because they are much more fast-paced, in-depth, and at a higher level than they were the first time they took them. FWIW, students are allowed a drop/add type of period at the start of the year - so if you find that a particular class is not the best fit for you, then you can change to a higher or lower level.
Hope this helps!