The first thing you're going to want to do is better "gate" your sign-ups. The fact that you're not trying to learn anything about who is signing-up by either providing different CTA's on your landing page or by offering them a quick survey for faster access, means you won't know which users' feedback is closest to your "ideal" user.

In early experiments I've run like this, we've seen a 5 question survey get between 20-30% response rate as a means by which to get faster access to the product, so absolutely worth doing.

I like to run different types of users through a closed beta. "Patient Influencers" are people who can lend credibility to your business when in launch (either by testimonials, press, access to potential customers or investors) and the other are your most "real" users. What you're most looking to do is collect that product feedback and look for where these two groups' feedback overlap.

I have a lot of experience in early-stage product ideation and guiding it to product/market fit. I'd be happy to give you some more and contextually-relevant guidance in a call.