The best thing you can do is to try to walk them through sample questions of each from the perspective of a player. When can a player buzz? What effect does each part of the question have on what each player is thinking? How does the different structure of the questions reward knowledge (or not)? Try to show them how hoses and buzzer races work to penalize knowledge and reward luck or binary memorization (as opposed to learning real things about a subject).
Also emphasize how the pyramidal questions encourage students to learn more about each subject. Sometimes you'll run into an organization that specifically wants to penalize learning in which case you're screwed, but most educators have at least a modicum of passion for encouraging students to learn. Mention too that much of the quizbowl practice material out there is available free for all teams to use, including all of HSAPQ's past sets.
You may also want to enlist the aid of as many other people who like good quizbowl in the state as possible. One person is probably not going to be taken seriously, but a large group of voices from various places (especially coaches) can be quite valuable.
Finally, you may want to offer them options other than just HSAPQ. NAQT IS-A sets might work as a good bridge between super-short bad questions and the best pyramidal questions. As weird as it is, the "eyeball" test of how long a question looks seems to be a huge factor for people used to bad questions so don't think it has to be an "all or nothing" kind of change. Plus, it's very likely that if you go for a non-mathcomp provider that you'll get pushback on mathcomp; you may just want to agree to compromise on that and have them include it since some coaches (especially math ones) make that their single sticking point against pyramidal questions.