95% accuracy with Asterisk AMD??! We've never gotten above 80% accuracy on Asterisk AMD with live dialing for a client, and that was with the 3+ second analysis time and a very high drop rate. What kind of sample size were you doing that with William?
As for Sangoma CPD/CPA/Lyra, it can be a pain to set up and manage, and it doesn't work with all carriers. But it is able to do pre-Answer call analysis, which is the big thing missing in Asterisk AMD, as well as Lyra being much faster as far as post-Answer analysis.
If you want to know more about how it works, just send in an email to firstname.lastname@example.org
and we'll get back to you today.