I still think another AP would be helpful, but in the end it’s up to you.
I think you’d have the strongest chance at getting into somewhere like St Andrew’s, which likes US applicants. Oxford’s a reach for eeryone, because just having the stats and recs only gets you so far.
Have you looked at the past HAT papers? If not: https://www.history.ox.ac.uk/history-aptitude-test-hat#collapse1-4
Work on your Personal Statement- do some research online, b/c it’s different than a US essay. Do a decent job of that & my guess is that you will get unconditionals from Edinburgh & UCL
Oxford is a wild card. @Conformist1688 is right that you should check out the HAT sample papers & marking- it is an important part of the cut for interviews.
I wouldn’t go for St Andrews for the same reason that Conformist is recommending it: so many Americans 
Consider adding Durham: very strong for History, collegiate (ie, you belong to a college within the university, as you do at Oxford & Cambridge), nice undergrad experience.
Definitely do the past HATs under real conditions. Doing sample MATs and getting results in the 80s were both a big confidence boost for my son and a good indicator for his potential success with the process.
Thanks for the info!
As stated earlier, my GPA is on the low side (at only a 3.75). Thus, IMO I think I’d have a better chance at getting into Oxford than at SA. (SA looks at GPAs)
P.S. Thanks for the link! 
Thanks for the insightful reply!
Can you give your opinion on LSE as well?
An unweighted 3.75 is not an the low side. I don’t see any way you would not get unconditional at St. Andrews and Durham unless you blow the essay.
(opinion) LSE isn’t my first choice for undergrad, I think it’s a better grad school experience.
Whoops, let me clarify.
What do you think are my chances of gaining admission to LSE?
To meet the minimum requirements you need another ‘preferred’ AP with a score of 5.
St. A’s would be easier for an American to get in to than Oxbridge or LSE, regardless of whether your GPA is taken in to account or not.
Would AP Psychology be a good choice?
It won’t hurt, but in the past it hasn’t taken very seriously. Until last year it only counted as 1/2 an AP & even though it now counts as a full AP, for a subject that it doesn’t relate to it won’t particularly help (possible exception is unis (other than Cambridge) requiring 5 APs, where you already have taken all the relevant ones).
Thanks for the insightful reply!
I need further help regarding what colleges I should put on my UCAS application. Right now these are my top choices based on my current stats.
I’m well aware that I can only put five universities on my UCAS application. Based on these seven choices, which five should I put?
Oxbridge and LSE are chancy for almost anyone while the rest are likely if you hit the requirements so choose based off of personal preferences.
No one can decide for you whether you would prefer England vs. Scotland or a city uni with no real campus vs. a collegiate uni vs. a city uni with a campus-feel any more than someone can tell me whether I like vanilla or chocolate ice cream better.
Thanks for the reply!
I’m actually not that concerned with the campus environment, to be completely honest with you. What I care most about is what’s taught and how a school will shape one’s outlook on life.
Please correct me if I’m wrong, but I’m going to make the assumption that I have the stats. to get unconditionals from all except Oxford and LSE. Please forgive me if I’m repetitive, but I just want to confirm that I have everything in order so that I’ll get an acceptance from at least one of the above schools.
Also, I think I phrased my quite question poorly. What I meant to say was that I would like to have a list of schools in which I would have the maximum chance of getting into. This would give me more flexibility to decide whether I want to go to a school or not as well as more of a choice in deciding which school I’d want to go to. I hope this clarifies some things.
Chances are good anywhere other than Oxbridge/LSE, as stated before.
And someone correct me if I’m wrong, but you’ll likely be taught the same way in class at any UK uni besides Oxbridge (LSE tends to make everything more quantitative than everyone else, but that’s unlikely for history).
Hence the focus on environment, because what you learn and the impact on your outlook on life outside class will be shaped by your environment.
I am the mom of a graduate student so our experience might be different than that of an undergraduate applicant. My son applied to and was accepted into both Oxford and LSE. He opted for Oxford and is very pleased with his selection.
It is wonderful that you have will have strong recommendations from your teachers. Please keep in mind that not everyone excels at writing a solid recommendation. Make sure to give your selections some serious thought after you find out how many you are allowed to submit.
Here was our experience regarding references. Universities want to hear from people with whom you have discussed your motivation for the proposed program, who know your academic work, who can relate how well your studies up to this point have prepared you to be successful in your intended degree program. They are looking to learn about your intellectual ability, if you have the capacity for original thinking, how strong are your written and oral communication skills, etc. and do you fall in the top 5, 10 or 25% of those categories. You are applying to schools than really want to know that you will be successful in your future studies.
Good luck!