Thematically Calvary Rifles might be a better fit since its Rifle Company. It's also kind of goofy to have both RE Flamers AND Ass Engi flamers in the same commander. There is also significant overlap with Rifles being able to lay mines as well as the engineers. I do agree that it would be nice to have Ass Engis in more than one commander along with the other 1 off Doctrinal units that you mentioned.
Maybe could replace RE Flamethrower be RE rifle grenade?
Or maybe replace by ranger and try give LMG upgrade?