Pay-per-call Companies that record the calls?

I need a recommendation for a service provider.

I create websites and drive organic and paid traffic to my local clients' sites (they are usually professionals who need new clients). I pay for the clicks, and clients pay me on a per-lead basis.

However, I need a better solution than Freedom Voice offers for trackable, local phone numbers. I need the calls that I generate to be recorded so I can discern the names of the callers myself. My client's staff don't keep track of these things well enough, and I constantly have to "prove" to them that my leads are becoming paying clients. It's quite annoying.

I would also like the system to have data export capability ("You received X number of calls this month - here they are").

An added bonus would be if the system could auto-bill my clients based on the number of calls I generated for them during the month.

Anyway, I know that such a system must be out there, but I'm not sure where to look or what terms to search for. I know there are companies like Ring Revenue (pay-per-call), but I'm not sure if those are appropriate solutions for what I'm doing, or if they are mainly for affiliate referral people (not really what I do). Or, those kinds of companies could be appropriate, but they could be too expensive for me.

I would sincerely appreciate any guidance you could suggest.

Bob