No, no, let him wear both!! Then reduce his Defense Pool by the sum of the maximum recoil/movement modifiers that they can compensate for!!
Gross stupidity is its own reward.
If he whines, go get Aliens. Cut to the scene where the two heavy gunners are doing their armature-exercises on the ship pre-drop, making sure the gear still works. Ask him if he really thinks he can dodge, even a little bit, while wearing not one but two of those suckers. Laugh with amusement if he says he does - then smack him with the phone book and tell him to learn.
Dual-wielding LMGs means it's pure spray-and-pray - suppression fire is the very best you can hope for, and even that is going to be heavily penalized, because of what everyone else is talking about. If he wants to wear two gyromounts, well - inform him you're going to use the 'sitting duck' rule, RG6, Run & Gun p.110. Because he's basically restraining himself, and a couple guys with pistols just became deadly to him ...