Assuming that there will be another background added to the game, I have put a lot of thought into what could be done. Here are the only real options after reviewing the source materials.
Armsman (Guardsman, Tempestus, Commissar)
This class would be a cross between the Tech-Adept and Crusader. Depending on armour used, you would get a set number of minion guardsmen. These would be very similar to those in a siege or rescue mission. However, as they are inquisitional minions, they should be able to be upgraded like Tech-Adept minions (possibly with existing weapons and items). An Armsman should be able to use all non-exotic weapons, and maybe some that are exotic. The Tempestus minions are more elite and can be given bigger guns, you get less of them than as a Guardsman. The Tempestus armour ability improves the minions ability to fight in some way. The Guardsman armour ability calls down an artillery strike (or minefield). The Commissar ability teleports in another minion, possibly having as many as in a siege. A special utility slot item would be “sidearm” that could be used to “sentence” one of your minions which would improve the fighting of the remaining ones. Play-style like the Commissar would be to summon more minions and kill them when needed. Another special utility slot item would be some sort of marker (portable vox?) that allowed the Guardsman to point his troops toward a particular enemy without reprogramming all existing weapons.
Pariah (Untouchable, Blank, Null)
This class would be a cross between the Psyker, Crusader, and Assassin. This class should be female as it would allow a null-maiden background (at least one that hasn’t taken the oath of silence yet). Since the class would use a smaller number of abilities than a psyker, it should have one armour type to allow an extra ability slot. The Null type armour would be the same as the sister of silence armour with some damage reduction or healing ability. The Blank armour should be something like a reduced version of a Culexus Assassin and look like the synthskin bodyglove. The Untouchable armour would provide some sort of physical push-back ability because even daemons fear a Pariah. The special utility slot ability should at least include psyk-out grenades.
Backgrounds considered unsuitable:
Too similar to the Crusader. Effectively the same role.
Too similar to Assassin and/or Crusader or the proposed Armsman.
All abilities can be done by the Pysker anyway, e.g. time stop, flamer without ammo, death beam, local teleport. Theoretical only, no recorded cases of Navigator Inquisitors. Much more common to be a Magos Inquisitor, and that didn’t even get done.
Not a combat role.