Surround the grumbles with few flak troopers. Problem solved.
No it's not, the long range of the Grumble means that it will be baited by Rocketeers / Gyros way before the Flak Troopers could engage them. And a single Kirov eating 7 missiles is ridiculous. The Grumble is stolen tech. It is meant to be powerful, but it is arguably the most situational and least effective of all the stolen techs.
So here's my proposal. Since the Grumble has 4 launch tubes, it would be only logical to give it 4 missiles (4 ammo) that it could fire in relatively quick succession. It is very important to give the Grumble the DistributedFire=yes tag, so it won't just fire all 4 at a single jet or something. Optionally, buff its damage against big air targets like the Kirov and Coronia's contraptions.
The Grumble should also never target Rocketeers and Gyrocopters unless it is ordered to do so. It can be done by messing with the warhead's effectiveness, and by using a dummy animation or something so the missile will still deal good damage to flying infantry.
I'm not sure if there's an intended weakness included even for Stolen Techs, but I think we would want even stolen units to have something that we can exploit to defeat them, otherwise we will have the whole OP complete ground denial Iron Dragon all over again.
Also I would say that it is rather balanced against Kirovs, since they are incredibly slow that you only need 3 or 4 Grumbles to take out the same amount of Kirovs. Only needing 1 or 2 Grumbles to have an area of guaranteed Anti-Kirov is far too OP I would say. And it's not like you can make more than one anyway... I would almost always make at least 4.
On another note, I realized Quetzal can pretty much bait all Grumbles without any cheap air units help, since they have their drones.