I, for myself, would use a Helicoil of the same thread for a couple of reasons. One is that the same studs can be used, but the other is mechanical. Though the threads are stripped, the remnants and interference effect of the original t.p.i. will remain. Changing to a coarser t.p.i. will cut across some of those grooves, removing more metal. Would that matter? I don’t know. The Helicoil BSF replacement uses the same pitch and will cut the existing threads deeper. This will give more bite. In addition, the coil insert is of hardened steel (stainless?), so it won’t strip and the only way it can strip is for it to pull out of the cast which will be harder to do.
Just a hint if you go the insert way. Run the insert down 3 or 4 turns and try the stud to make sure it is all seating correctly. It often helps to run a die or die nut down the stud thread to ensure it is precise as the coil profile is very accurate. The trap is that if something goes wrong, you can’t unwind the coil - you can only wind it through to the other side. If the hole goes through to the water cavity, no problem. If it is a blind hole, make sure you test the stud frequently.