Would it make sense to use a DC motor driver IC such as the TI DRV8829, to supply the iron with sine, or squared wave voltages?
The idea is that one may use a rectifier and a buck/boost to generate 24v DC (or even higher voltage) from (almost) whatever power supply he has. Power regulation may be achieved by limiting the supplied current (32level+direction).
It should be also possible to use the H-bridge to drive irons with "integrated tips". I wonder if hot air and desoldering tools can be controlled as well.