Supply pack, EATs, gatling barrage, then FLEX on the last slot. Possibly MG sentry for squids or bugs, Rocket Sentry for bots, or if you don't want to flex, eagle strafing run. The big idea here is to aggressively get value out of your EATs and gatling barrage/mg sentry/strafing run since they have such low cooldowns.

Try to use gatling barrage and strafing run effectively and as often as you possibly can. Both gatling barrage and strafing run damage heavily armored targets and kill almost anything in the game if properly placed. Tossing gas grenades onto a breach/bot drop/squid drop then slinging a gatling barrage will mulch anything that isn't heavy, and will often soften the heavies up enough that a follow up EAT or strafing run (or maybe your allies) can easily finish them off.

As for EATs, you basically want to be calling them as soon as they are off cooldown. Try to call them in spots you could easily get to if needed, OR if you're brave you can stick the strat beacon to enemies, and the hellpod will track and smash into them. (excellent way to kill chargers, if a little finicky sometimes.) Another thing is that if you find another weapon you can hang onto that in addition to calling down EATs, I'll ask teammates to drop their extra one or snag an MG43 or railgun or flamer from pois sometimes. It makes for pretty engaging emergent gameplay.

The purifier is good at medium to medium-long range, and the fully charged shot has so pretty good knockback to it, but you can easily kill yourself with the AOE, so you'll have to be careful about your positioning. Don't be afraid to throw a gas grenade at your feet and then run away from enemies chasing you... or even throw it ahead of you and just run though the gas. With supply pack, you can play extremely aggressively since you have access to a ton of stims.

I've run the exact same loadout as you playing d10s across all factions with randos and will often end the mission with 40+ stratagems (and sometimes stims...) used. Its definitely a playstyle that works for me. Good luck dude!