Going from Oxford back to US for finishing Bachelor's: What Econ programs should I apply?

You’ll be 2/3 of the way completed with your Oxford degree by the time you get transfer decisions from American colleges. The application deadlines for transfers is in Feb/March of each year, with decisions coming out by May. By that time you will have completed Trinity term 2020.

Then once you transfer to an American Uni, you’ll have a tough time completing your degree in 2 years, especially at places like UChicago and Columbia. Both of these colleges have core requirements. Although you may get partial credit for your PPE work, I doubt you’ll get anywhere near 2 full years of credit.

You may be better off just finishing the 3 year program at Oxford and then applying to Masters/PhD programs in the US.