AMI and SIP are different protocols. SIP peers can be both client and server in the same call. AMI is really intended for third party control, whereas your requirement is for first party control.
The normal way of invoking recording from a SP phone is use DTMF and features.conf.
If you really want to use AMI, and there is only ever one call per device, you could set the current channel for the device into a global variable named after the device.