Informal method one: Find someone who's never been there that you know, show them the new one, have them try to make a new account, watch where they get hung up.
Formal method one: Set up those "alternative" trial thingies I forget the name of, where one version of something is served to people following the link sometimes, and the other is shown the other times? I think that's how that works? And then look at time-before-leave-page and time-before-trying-to-sign-up, etc.
Of course, you could NOTE that you're adding tracking, temporarily, to try to make the page more usable.
Honestly -- and I know this will sound cynical, but it's the truth, AFAICT -- but no matter WHAT changes, some people always complain, no matter what. You literally cannot do anything without upsetting some nonzero number of users.
I know that might seem like advocating inaction or apathy, but it's meant more as a reminder that humans overall deal badly with change.
Stress scales used in psychology include "negative" events (like divorce) at change levels similar to "positive" events (like weddings). Stress, in some ways, isn't about improvement or worsening. Some of it's just about the change itself.
People vent a lot, or they'll have a bad day and piss and moan for a week about one button getting moved somewhere that helps fifty other people. Forty-nine of the fifty might say fuck all about the improvement, too.
this is mst3k