On the contrary of "go slower," I suggest you actually move faster. Bots cause issues when dropships come in. Sometimes, even when you're doing everything right, you can still get a flare set off, and if you're trying to clear a base and a dropship comes in, it gets a hell of a lot harder. The longer the mission goes on, the stronger the bot patrols and reinforcements get, so the best option is to treat almost everything like a blitz mission.

Most of what I'm gonna say, you probably already know given your loadout. The big difference between bot outposts and bug nests is that you don't need an angle for a guaranteed airstrike to take out a factory. If you're running the autocannon, you can take out factories if you're in front of them from a hell of a distance. Just aim for the upper part of the vent from within about 45 degrees of dead-on, and the factory goes up. If a flare goes off, it'll be dropped on the bot calling it in, and by the time they land, they won't have any idea where you are if you run. If you can't get line-of-sight on a vent, run up, call in an Eagle Airstrike, and run off again. For light and medium outposts, you can get in and out in no time.

For just regular patrols though, if you have to engage, engage at a distance. I'd swap out the mortar sentry for an autocannon sentry, mostly because it brings more immediate results, with less of a chance of killing you if the bots get too close. If you shoot at them from a distance, they're more likely to have less time to react, and not get a flare off, which again, is the worst outcome of engaging. Deal with it, and move on. Don't get bogged down in engagement.

Aside from that, the only real change I'd make is swapping out the orbital laser for the orbital rail cannon. You're not limited to just 3 uses, and while your autocannon can deal with sneak attacks on big bots, sometimes you just need to delete something. If they're close enough together, I've even seen it take out 2 hulks. You can get rid of a big threat every two and a half minutes, and not sacrifice speed. Only other difference between your loadout and mine is that I'm using the Liberator as my primary, but if you're happy with the Adjudicator, keep it.

For your team wanting to shoot everything, if they're going to insist on drawing aggro, let them. Do objectives, be proactive. You get a lot more bots from an area filled with outposts than an area empty of them, and you'll lessen the number they have to fight. Finish a spot, move onto the next, and do it fast.

One minor thing, factory striders. These things were built to withstand tons of air strikes, and even eat orbital lasers and rail cannons. But if you take off the machine guns on its chin, and walk up to it and unload on its belly with the autocannon, they go down very fast. The biggest challenge will be getting your team to stop calling in airstrikes so you can do it.