The solution to counter cons spam and USF is clearly the sniper, as 1,2 or 3 unit in your BO. But the sniper is a mandatory unit to play Ostheer today and still after the next patch.
Bear with it and learn to play with.
This seems incredibly risky and I think the sniper should only be deployed as a mid to late game unit once you've secured your territory and have a proper combined arms force.
Not only do you limit map control, capping power and holding power, but it leaves you incredibly open to the LT/M20 push. You generally want to rush out that T2, or at least, I think that's what people still do vs USF. Against Con spam it'll work against the supports/elites who will inevitably support it, but just shooting the cons themselves, you've got to deal with another squad and a half and with things like Oorrahh!, you have a lot less breathing space to operate and are really depending on an MG42 to shut down more than one squad to even the fight when the big engagement of infantry occurs.