No, unfortunately, you can't actually "change to a different partner" .... what they are offering to do is, in reality, the same as cancelling the old account (thereby losing all accumulated points) and setting up a new account.

Also, there is no worthwhile way to transfer United air miles to HHonors points.

It's well documented here (and elsewhere; i.e. the e-Miles FAQ) that you need to join e-Miles using a signup offer from the place you want to receive the benefits; i.e. in your case, signup using Hilton as the partner.