truerunner, I didn’t realize UCAS allowed students to cancel AP scores, but putting that issue side, my son did just what you are proposing. He didn’t receive an offer after the first Oxford interview, then enrolled at another university, then reapplied (TSA again, shortlisted again)… and the second time was the charm. He just started his second year at Oxford.
His situation was a bit different in that he had actually planned to study at UCL. (He got offers from two programs at U of Edinburgh, one at King’s and one at UCL, in addition to the Oxford rejection.) After his senior year in high school, he attended a summer “boot camp” for students with ADHD who were either already attending university or just about to start… and he met a kid who had crapped out in his first year at King’s… and that kid warned that London had been a pretty challenging place to start his university life. He advised my son to start at an American university first-- to learn how to live independently, figure out what support services were needed, learn how to manage time on his own (etc.), without having to simultaneously navigate a different culture (that expects more autonomy from university students ) while adjusting to a huge and somewhat overwhelming city, living in accommodations that are quite different from the American dorm experience. We had put down a deposit for UCSB, anyway-- just in case, since my son had already been unsure if he was ready for London straightaway, and we also thought he could use more academic preparation in science for his degree in psychology, especially since he may decide to attend medical school in the future and will need science and math credits from an American university. He then proceeded to get permission from UCL to defer a year, but unfortunately (ultimately, fortunately!), something went awry, and the admissions people at UCL thought he was enrolling instead of deferring. When he started getting email welcoming him to UCL, at first he thought it was just a mistake… until he eventually got a welcoming FB message from the head of the student psychology society! He tried to get it sorted out… and thought he had been successful… but it turns out deferring admissions also involves UCAS, and he had missed the UCAS deadline for deferring, so he had to reapply through UCAS for the next cycle!
My son didn’t find out he had to reapply for UCL until about a week before the Oxford deadline. Like you, he had previously requested feedback from his Oxford interviewers, and they said his TSA score, PS, reference, academic preparation, interest in the subject and non-tutorial parts of the interviews were strong, but he was weak on the tutorial part. They also said it could be worth reapplying, but it would be better to apply to a different college. Since he now had to go through another UCAS application cycle anyway, he decided to give his dream school another shot, but he had to hurry to update his PS (which included briefly explaining that a year at an American university would better prepare him academically for his course in the UK), get his referee to update her reference (she was on sabbatical in Mexico!) and find somewhere to take the TSA. When he was again shortlisted, the interview process went much more smoothly. This time around, he had already finished his quarter (and finals) at UCSB, whereas the previous year, he had to leave for interviews rights when his first semester (of senior HS year) finals were starting… and some teachers were not very happy (or accommodating). He had to finish final assignments and work on group final projects and study for finals while in Oxford for the interviews, but students being interviewed weren’t allowed internet access at the college where he was staying… and his phone wasn’t working there, either! So, he had to keep rushing over to my hotel for the Wi-Fi, which made the whole situation even more stressful than the usual (inherently stressful) situation. (Plus, his second interview was delayed, and his short-acting ADHD medication had fizzled out by the time of the interview-- and he hadn’t brought any extra with him!) Again, things went much more smoothly the second time, and he got an offer!
If you are allowed to cancel AP scores… it appears you already have 6 fives? Law doesn’t have particular subject requirements, except to show you can do well in a course with essays (like AP Lang) and to to demonstrate some proficiency in math, which you have also done, so it seems you are more than meeting the requirements with the 6 fives. If you think not having the AP Lit score is a disadvantage, you could still take an SAT Subject exam in Lit while at your university (I think Oxford wants a score of 720 or above), and get your referee to make a (favorable!) prediction. You can look at the schedule, but there is an SAT Lit exam in December and a couple more in the spring, I think. The five in AP Lang is probably more valuable, though… and sufficient.
You might also want to look online for Oxford interview prep. It’s possible to find tutors who studied law at Oxford who can give you interview pointers, do a mock tutorial with you (by Skype or in-person in London, if you have any time before interviews)… and give you feedback.
Good luck!