What about adding some long range fire into the mix? Didn't the red army have platoons armed with nothing but submachine guns supported by a rifle and mg armed group? The ballistic characteristics of that PPsh SMG would be pretty close to the P90, so it's not a bad match.

Add in some long range rifles into the mix (not assault rifles) and you'd have a workable organization. Not one per team, but supporting the MG equipped teams. The MG teams would have a longer range, but they'd use that to stay far away. The MGL teams would work up close and do the assault/breach thing.

I'd propose doubling the LMGs in the heavy teams to two and giving the remaining members of those teams long rifles. That would answer any long range concerns. The unit as a whole is still better off because the light teams have gotten so much lighter.