If people can use your product before signing up, how do you attribute the signup?

Attribution problem I haven't solved, for anyone running a try-before-signup flow.

Last week I took the account requirement off the front of my product. You can now use the main thing without signing up; the account is only needed to export what you made. It was clearly right for the product — nobody understood it from a description, and they understood it immediately once they'd used it on something of their own.

My measurement fell apart the same week.

• Top of funnel widened, conversion rate collapsed, and neither number is comparable to the month before. I don't have a trend line any more, I have two unrelated datasets.

• The compute is real, and it's spent on people I can't identify, can't email and can't count. Costs moved before any of the good numbers did.

• Worst one: somebody tries it anonymously, leaves, comes back four days later and signs up. In analytics that's a cold direct signup. Whatever actually did the work gets credited with nothing.

What I've tried so far: rate-limiting on something other than an account, so the free tier survives without a login; putting the gate on the output rather than the input; and simply accepting first-touch as lost.

I'm stuck on that last one, because both obvious fixes are bad. Fingerprinting is creepy and I don't want to do it. An email capture on the anonymous path just rebuilds the wall I removed, one step later.

Two questions for anyone who's been through this:

1. What do you actually use to link an anonymous session to the account it later becomes, without making the anonymous part feel surveilled?

2. Did your conversion rate ever become a number you trusted again, or did you give up and start measuring something else entirely?