I think a couple big questions that need to be answered by the OP is “what do I want out of life and what goals do I have in life?”
I agree that the English system (where, with a few exceptions, undergrad is essentially junior grad school) is not great for students who want to explore different interests and figure out what they like (Scottish system is a bit better in this regard, though still not as flexible as the North American system).
Speaking of which, I wouldn’t ignore the undergrad-focused liberal arts unis (they’re essentially public LACs) in Canada, like Mount Allison, which has produced more Rhodes Scholars than any American LAC.
They would be cheaper than full-pay at a private LAC in the US (possibly on par with a private LAC with scholarship).
But the benefit of a LAC is mostly in the first 2 years. You’re expected to find a major by your 3rd of 4 years.
BTW, in the UK, both KCL and Warwick offer a Liberal Arts degree and UCL has a Social Sciences degree.
But honestly, even if you aren’t in love with Linguistics, remember that your life doesn’t end at undergrad. You could always explore a masters program (or many). They don’t have to be in linguistics. You can explore masters programs in the US. Business programs tend to be pretty generalistic and cover various fields, for instance. Can you articulate what you dislike about studying linguistics and what about “the liberal arts” (which, BTW, yes, both linguistics and the sciences would fall under) you find attractive?
And where do you have citizenship/permanent residency? In terms of working, it’s not so much where you want to as much where can you. If you’re not American and not studying CS (or a quantitative grad degree), staying in the US and finding a job will be very challenging (unless you marry an American).
Given all that, I’m not all that sure of the wisdom of trying to transfer to the US (or starting all over again), spending a ton of money, giving up an Oxbridge degree, and then what, exactly? Would that leave you better off than staying at Oxbridge to finish up? How exactly?