I'm looking at starting with USPS, FedEx, and UPS

Out of curiosity, how are you doing this? IIRC a few years ago when I was playing around with the FedEx API it explicitly forbade using it for price comparison with other carriers.

Are there aggregator APIs that you're using? Or have the T&C changed?

It is still the same, you can't even have other carrier rates near UPS rates.