I think you’ll do better in the U.K., since the SAT and AP scores are what matter. But Oxford, Imperial and UCL are probably still out of reach (Imperial is a tougher admit than UCL).
Add some more universities that are comparable to Edinburgh. Maybe Durham and St Andrews, since you appear to be keen on prestige, and KCL if you like London. If limiting your list to 5 UCAS schools, you should drop Oxford and/or Imperial.
You will need a reference from a math teacher, the one you have senior year (your “favorite”) could work if you drop Oxford and only need to apply in Dec/Jan.