Actually you sound like a good candidate for admission to some R1 university in the US. But the higher ranked the institution is, the tougher the competition, and in some cases the smaller then entering cohort.
In the next cycle, I suggest making a broader search, covering universities down to at least the 50th ranked, maybe a bit more. You don't need to limit yourself there, but include some. Note that if you are rejected by some place then you are more likely to also be rejected by very similar places. State universities tend to have larger entry cohorts than some others, also.
In the interim, make sure you keep contact with those professors who now support you. If you lose contact they will start to forget your merits.
If you don't need an income, such as with family support, see if you can take on some informal research project with the aim of writing a paper. Even a survey paper for some sub field will give you some practice, though it might not be publishable. It is harder if you need income, since there aren't many jobs that you are qualified for. My daughter, in a different field and for different reasons, got a job in an academic library to fill some time, earn some money, and keep her "academia adjacent" for a year or so while she made decisions. She is now a professor.
But, keep active if possible, keep close to supporters, cast a wide net.
Good luck.
Of your three suggestions, the first doesn't seem very good in terms of your current goals. The others are better, but it might be hard (late) to get connected to one of them. You won't get much research experience in a year, but you could get a better idea of what research is really like. If you are near a major university and can take advanced courses as a non-matriculated student it might let you learn a few things.