Ok. First off while force 7's are high end they are quite doable. Especially if they aren't bound. If they are bound(which is required to make them work for someone other than the caster) it would probably take a high end level 1 initiate with a focus to bind them. The Yaks certainly have a guy or two like that though.
Anyway I think you're fine.
First off you don't neccesarily die in SR4. You just lose a point of edge. There is a thread going into detail on that around here somewhere.
Secondly you need to remember that "immunity to normal weapons" doesn't actually provide immunity. Just good protection. In this case 14 points of hardend armor.
But hardened armor also isn't as hard in this edition, because your successes add to the effective DV. Also lots of stuff gets AP, very noticably electrical attacks, halve armor (so the ghostbusters had it right all along)
Oh and another important caveat, they erratad the spirits. Their stats are now under control. Equally importantly don't forget that if they materialize that takes a complex action. So everyone gets a free shot at them before they can do anything.
Anyway so the point is that lets say you've got a simple sammy with a ruger warhawk that's only loaded with (erratad) regular explosive. so 6DV -3AP. He uses edge on the attack and so rolls a healthy, say, 18 die with exploding 6's and +4 damage for a called shot. Generating seven hits fairly likely. Reaction depends on spirit type but lets say that it gets 3 hits. That leaves you with a final DV of 6+4+7-3=14. Which with the -3AP gets through the things armor.
Of course it'll probably resist maybe seven of that so it'll only take 7 damage. So it'd take a couple warhawk shots to finish the thing. But if the players have tasers, assault rifles or sniper rifles, APDS/S&S or something they might be able to oneshot the things (or oneburst them).
And a mage can also one shot them with just a little overcasting. You mentioned the adpets can too. Though they may do better with guns than astral combat, and the spirits might no close to killing hands range.
As for the close combat specialist he is probably not as effective as he looks on paper so long as a CC player is going toe to toe with them. This is a game of ranged combat not melee. They're still fun though
If the grunts are only rolling nine dice they shouldn't be a huge threat so long as the players are smart and don't get shot at by all of them a once. Unless surprised they could always go on full defense with edge to avoid getting hit.
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The third and most important point is that SR is a tactical, deadly game. If this group is setting an ambush that's a while different story. Even with edge it's quite possible a few PCs will be surprised and then they may be screwed.
Conversly if the PCs ambush this group they'll go down fast. (Mage manaballs a couple spirits and some goons, someone with a grenade gets the rest of the goons, sammies slice through the CC specialist and the last spirit.
It also makes a huge difference what weaponry the team has, obviously. Especially for the spirits.
If this is a tactically balanced match up I predict it will be exciting and that PCs will be spending edge to get out cleanly, and maybe a trauma patch will be needed.
But again the worse cas scenario is just a lost point of edge from everyone to have lonestar or some mafia happen to show up and run the yaks off.
Oh and you mentioned they are soft on game mechanics. This would be a good oportunity to strengthen them up. Give them solid tactical advise that their char should know. Like when to go for the +4 called shot bonus and when not to. Also get them diving behind cover and get some range/vision mods to easily take out the goons. Be sure to tell them to use full defense if they're about to get slaughtered by something. Also remind them of uses for edge. For example spirits are typically loath to use edge when the aren't in danger of more than being disrupted. So if everyone in the team spends an edge to go first they'll probably get to go first (except if the yak hitman spends edge), and that first action will probably take out half of the hit squad force right there.
Of course maybe your PC chars are weak. If you're really worried try running the combat yourself.