As I see it... types are not "included" in an FI rating. In your licence it just says "FLIGHT INSTRUCTOR". And all your type ratings are listed in the usual place.
I think the "15 hour" rule is a CAA made-up rule. And I am sure if you do your type rating test/renewal with a "Flight Instructor Examiner" (FIE) you are exempt from the "15 hour" rule.
But you better ask Fred Cross.
This is why LASORS is useless. It's not UK law, its a 'summary' of the CAA's intepretation of JAR FCL and the ANO.
Come to that, even JAR is not law. In fact, the JAA doesn't exist anymore. Everything is now governed by EASA.
Confused?
And we wonder where all the money goes