So I updated to iOS 8 and thought I'd give this another try. To my surprise, I actually did get a response in my baseband log:
73.289 sms: GSM SMS Point to Point PDU (as hex str): 440c9144...ae08
73.289 sms: MT SMS Message details:
73.289 sms: Message ID: 0
73.289 sms: Sender: +447786205094
73.289 sms: MC Timestamp: Y:2014 M:09 D:17 @ 21:35:14 (Offset:-240, DST:no)
73.289 sms: MC Timestamp: 1410989714
73.289 sms: Source Port: 0
73.289 sms: Dest Port: 5497
73.289 sms: Msg Encoding: 4 (Binary)
73.289 sms: Body Length: 88
73.290 sms: Raw message was successfully parsed, and the message is valid
73.290 sms: Sending manual ack (pdu parsing succeeded)
73.290 sms: Acking messageID 0 with success and is temporary on mode GW
73.290 sms: ACKing an SMS on signaling
After pasting the hex string into the form it appears the silent activation SMS message was sent to the correct phone number: "Silent activation SMS has been generated and will be sent to 416*******. If all steps were performed correctly, iMessage will activate within a minute." It's been several minutes now though (15+) and iMessage never actually activated.
So close!