My ground game is fine even in unfavorable conditions (surrounded with no cover) until the reinforcements arrive. The difficulty until then is in the sheer volume, which I am fine with. The reinforcements just seem like an extra FU in a map that's already difficult as is. And it doesn't matter if they spawn 10+ squares away when they get a free turn. You know, with firearms. Also, they spawned in all 4 corners of the map, specifically surrounding my troops. And if the turn they spawn on isn't predictable, how am I supposed to know when to pop smoke? This are rhetorical questions; the answer is you don't; you either keep all your troops crammed in smoke the whole fight (how many s'nades do you expect me to carry?) thus inviting frags every single round or you just don't use smoke and die. This is another case where it's made out to be easier than it actually is because you may be operating with better tech, more troops, etc. I am running 10 agents with Galils and Liquidators. (Why would I use up a seat for a drone or a dog, honestly? I want actual firepower. Humans can carry guns, bombs, medical, and motion sensors. I'll pay for the agents.)
I can only tell you what has worked rather well for me. If you want to play your own style, that's your choice. In my current SH Ironman game, I've already dealt with 10 manors without problems. (They keep popping up, because for some reason I haven't gotten Dagon and Exalt forward base missions in 12+ months.)
You don't go to manors with 10 people. You'll need Osprey (16 seats) or Kitsune (15 seats). Then you have enough room for ~2 scout drones and ~1-2 dogs. The benefit of scout drones is that they can see through smoke, so if you use the smoking tactic, they are very useful. Dogs, when trained a bit, have good TUs and sniffing is quick. So they can each turn run about 10 squares away, sniff to spot the enemies, and come back to cover.
You'll pop smoke in turn 1. You'll need to drop or throw at least 10 smokes to create a sufficient perimeter (which also slows down enemy units advancing on you). The smoke starts to clear in 7-8 turns so you'll likely need to renew it then. So 20-30 preprimed smoke grenades should be enough (I usually give each agent either 2 or 3).
You'll stay in the smoke for at least 10 turns, possibly more. When you have killed most of them using grenades, dynamites and hi-ex (pre-prime at least some of them), and dozens of enemies start panicking, you may consider letting the smoke go off and switch to sniping the enemies instead.
I think you're behind the tech curve if you use Galils. You'll want BO sniper rifles or auto-sniper rifles. With maximised accuracy (90-100), these sniper rifles are accurate enough to reliably hit the enemies even through the smoke when they personally don't see the enemy units. This is especially useful against Black Lotus (because you can shoot the followers, warriors and assassins).
At some point, you may need to go out to search for the last remaining units, especially the ones that cannot surrender. Most of the times the battle is over in 10-15 turns.
Reinforcements are no problem if you are still in the smoke when they come. You'll just throw explosives at them if you want to be sure.
The most unfortunate thing is if almost all enemies are panicking and you switch to sweep mode to clear the last few of them, and the reinforcement arrive then. You'll have to be prepared for that.
This is an essentially guaranteed recipe for dealing with manors.