I did some experiments with the special H bridge timer functions on a STM32 series controller, you can specify the "dead time", this is the time the two sections (A and B) are both off. It worked, choosing a longer dead time's even controlled the total output power of the filament. So you have a software controlled filament driver. I have added the AC coupler and virtual center tap in this schematic, but you get the idea. By using fets's the efficiency of this circuit is high, but the down side is you have to have the dead time. Use a scope to observe the behavior of the brigde, not having the timing right can lead to strange effect and high power consumption.
The selection of the fet's are just what I had laying arround in my parts drawer. Other types could do the job also.