lanzhounoodles Competition wise there are things like the science olympiads, big science competition, jso (junior science olympiad). Although you'll probably get the results/do the main science olympiads too late for the interview, but it should be fine for jso and bsc. There's also icas as well, and it might be worth doing both icas science and math.
For maths/coding related stuff besides the amc, you could do the cat (computational and algorithmic competition) altho its results might come out too late. There's a lot of other competitions that the AMT (organiser of math/ coding comps like amc) offers that you should take a look at. Ofc you said that your school doesn't offer much besides amc, so to do these comps, just ask your school if they could do the competition at your school, otherwise ask if you could do the competition at some other school that does offer it.
