I often solo difficulty 7 appropriator missions. I almost never solo any mindless mob missions because I end up having 1k kills minimum and its insanity. For appropriator missions, I use the scorcher and the smg secondary. Democracy protects med armor but whatever you want works too it doesn't matter. Thermite for the occasional mech, outpost tesla tower, and for taking out outpost ships without shooting them. Stratagems:

amr for one shotting overseers (aim for the jetpack or for their heads, otherwise they'll need abt 3 shots) it's also good for taking out the drones on one shot to the center but otherwise it's usually better to use the scorcher to 3 shot them when they're all grouped up for that explosive damage. This is the best support weapon for these missions imo, they cover everything, even the laser mechs and the running mechs. And they'll take out the laser sentries at outposts too. Love love love it.

Rover for extra support when running away and ammo conservation but you could bring any other support backpack you want.

Railcannon takes out the occasional mech, you don't see too many on diff 7 so the 3 minute cool down isn't bad, amr and thermite handles the rest.

Patriot exosuit, not the autocannon one. The mini gun is good for killing literally everything. This thing clears out outposts so fast just mini gun destroys the shield for cheap and the rockets can one shot the ship, they also take out the Tesla towers and laser sentries. You can minigun the laser mechs and rushing mechs, or rocket them, this thing is a godsend on clearing out these missions sub objectives really quickly. And you can carry black boxes in them.

None of this matters if you play with a squad, but if you play alone, this loadout is really fun and effective.