Again without knowing the fields or subfields you are looking at, it is hard to make specific suggestions, so I will instead point you to the resource I mentioned before, Edurank, and suggest how you could use it.
Edurank’s field and subfield rankings are purely research publication based. That is very crude, but it is also empirical and rigorous, so I like it for that reason. Obviously you should treat this as merely one possible starting point, and go into specific departmental and faculty webpages once you have identified some possibilities.
Anyway, as noted I don’t know your interests, but you mentioned STEM, and I know Penn and Columbia are both strong in Bio research, so we can use that as an example:
Sure enough, in the US, Penn is at #8, and Columbia at #15, so that is very good. But using 2023-24 CDS data, Penn had a 4.6% transfer admit rate, and for Columbia it was 10.1%. These are typically extremely competitive pools, so many students who have done well in college so far will not be admitted as transfers.
Fortunately, however, some very good publics are also high on that list. They include institutions like Washington at #5 (46.1% transfer admit rate), Wisconsin at #13 (47.5%), and Minnesota at #16 (52.6%). Obviously these are not guaranteed either, but I think it is fair to say publics like this are, among other things, quite interested in your sort of case–a very good student who ends up feeling like they are at the wrong sort of college, or at least at a college with the wrong sort of department given their emerging interests, and who would benefit from transferring to a college with the right sort of department.
Of course this is not to say I know Penn or Columbia won’t admit you as a transfer. And I chose Biology, not you, so obviously you might get a different list with a different field or subfield. But for pretty much every field or subfield I am aware of in which Penn and Columbia would do well by this measure, so would some publics with much higher transfer acceptance rates.
Of course if you would rather stay at your LAC than go to such a public, that is entirely up to you. But since you are talking about things like the quality of the research program, I thought it was worth pointing out there are usually these departments doing great research which are at institutions more open to transfer cases just like yours.