Or turn it around a bit. If the entire device could operate at high pressure, then one could imagine putting it inside a jet or rocket engine. Feed it compressed fuel/air mix, burn, extract some energy via thermophotovoltaics, and blast the exhaust out a nozzle or use it to spin a turbine to drive a bypass fan.

An obvious down side is that most jets have very, very high fuel flow and power output, and the area required to extract enough electricity to make this whole exercise worthwhile may be excessive. Also, a lot of military applications are not going to like that sodium illuminant lighting up the exhaust gasses, scattering radar, or otherwise making the plane more visible.

edit: I see that there’s an effort to recirculate the sodium. Maybe that’s enough.