I never thought of this one but your first solution sounds pretty great to me. I know SE will never have the guts to go for a no recast skill tied to resources because they've been systematically trying to cull down that kind of things all across the board, but I'd still think that having a complete, free agency into how you use FT and when would be a blast. Build heat first, then spend it, at the cost of no mobility.

Either way I could even just settle for a fixed gauge cost and keeping its 60s timer really.

Getting a free hypercharge at the end would be nice as well, but that would become tricky due to the single target rotation suddenly benefiting from it, unless you require a specific amount of ticks to go through perhaps. But then, the frustration when you have to move before getting all your ticks?