Usually, that latter function is served by the contact form. The intent of the site is to give them just enough info that they are motivated to contact us to learn more, after which they go in our CRM (Close.io, following @patio11's recommendation of it) and get extensive follow-up over what is, as you correctly surmised, often a very protracted evaluation and sales cycle. It's not uncommon for the subsequent back-and-forth to take months or, in some cases, even years, before (if) there is any real traction.

My organic traffic behaves about as I expect; they often fill out the contact form and we end up having a productive chat. Paid ad traffic, however, unfailingly bounces.

The problem is in your approach. Try switching from asking to giving in exchange for email. Then nurture the lead through email and you'll see much better results. The money is in the lists.

Thanks for the tip. But how do you suggest, within the logic of the site and my product, that I give in exchange for email? What should I offer? I can't just wall off all information behind a demand for contact info. If they have no inkling of what's behind the wall, there's no reason for them to provide it.