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.