At $9 with $7 loaded cost and $180 a month of tooling, you're at roughly $0.90 an hour of contribution before any supervision time, and supervision is real once AI output needs review. That's not a price, that's a favor with an invoice attached.
The claim you're being asked to accept is that the demo's performance transfers to this client's data. AI SDR demos run on clean, opted-in lists. Your client's list is skip-traced, and if 40 to 60% of the numbers are wrong or disconnected, the tool's advantage shrinks to the dialing itself, which was never the expensive part. Ask them to run the tool on 500 records of their own list and compare connected conversations per hundred against what your seat produces. Either the number supports their ask or it doesn't, and you stop arguing about philosophy.
Unbundling the tooling is the cleaner first move. Show the $180 as a line and price labor at what labor costs. It reframes the conversation from your margin to their stack, and it makes the second client's eventual comparison easier to explain because the rate card is the same for both.
Outcome pricing does something you may not want. Per appointment moves list quality risk onto you while payroll stays fixed, so a bad data month hits your payroll rather than their budget. If you go there, cap it: a floor per seat plus a bonus per qualified appointment, with "qualified" defined in writing before the first invoice.
Separately, eight months of market knowledge living in one person's head is a single point of failure regardless of how this pricing lands. Get the street-level notes into your own documentation while she's still on the seat.