I'd model it as a Conviction roll, allowing you to use your highest Power Specialization to add to it. For each successful roll, you get to keep that many shifts. For example, Harry, who's Conviction is Fantastic and has a +2 Specialization in Fire, which brings him up to Legendary. He rolls Conviction at Legendary for let's say 5 exchanges, and gets a +8, +8, +7, +10, and +11, for a total of 44 shifts. Once he gets inside the Sign, this is all he's got for spellcasting.