Probably not if one runway is getting the bulk of traffic, the big problem at KLGA is traffic having to cross 13/31 to get to 22 while traffic maybe landing on 31, here we use the diamond crossing technique for the paths across a runway, you get near misses with landing aircraft but get a better flow,
be the same with a wind change, traffic will have to cross 4/22 to get to 13, i find it odd that the bulk of the parked aircraft are nearer to 13/31, just check that 13/31 is open for takeoff/landing i don't remember having this problem
how about closing "Both" ends of 4/22 for "take off" only to force 31 to be used for take off, maybe worth a try if 31 is not used much for landing