I think the consensus here is that it is not a good use of your time unless you a) can provide Columbia with a compelling reason why you want to transfer and b) can provide decent LORs.
The former is because reach schools don’t seem to really want to accept transfers “just because”. They need to know that your current situation can’t provide the academic or collegiate experience that you want. Since Chicago and Columbia are pretty similar in both rigor and environment, it may be difficult to determine and articulate what Columbia offers that Chicago can’t.
The latter is because LORs are supposed to provide information that isn’t readily available from other parts of your application. Your record shows that you are a strong student. It would be helpful if your LORs can go beyond that.
I believe that you have gotten answers to this specific question. We think that your academic profile is very strong, but the chances of successfully transferring to Columbia as an undergraduate student are bleak unless you can articulate a compelling academic reason that you want to make this transfer. You do not need to give us a compelling academic reason for the transfer, but you will need to articulate this to Columbia if you want to improve your chances of being accepted.
The two things that you can do to improve your chances would be to figure out what this reason is, and find people who will give you strong letters of reference to support your application.
If you don’t mind sharing, what is it about UChicago that you don’t like?
I ask because… UChicago and Columbia are academic peers and are quite a lot alike in a number of ways. You would be transferring from one orange to another orange.