After spending an entire Saturday working on the heating circuit, I finally figured out what was causing the fuse to blow repeatedly on my dryer. It wasn't the fuse itself or the element, but the thermistor reading incorrectly.
I pulled the main control board and checked the resistance of the temperture sensor. It was way off spec compared to the factory range. Since replacing the board seemed like a major expense and hassle, I decided to try and swap just the thermistor first. It was a tiny part, fiddly, but manageable.
Swapped out the old piece, reconnected everythign, and ran several cycles. The control panel now holds the heat for the full cycle without tripping the safety device. It feels much better to have it running properly instead of worrying about the next fuse failure.