out of control fig after restoration pruning in February

After a couple of years of not pruning my fig, but getting nice slow growth and adequate figs, I decided to try to get it into shape and do it properly last February.  Now I feel it's out of control. Masses of new growth, what seems like hundreds of figs and it's overrunning everything nearby.  I have a quince next to it, which is being overwhelmed.  Can I trim it back now as many of the branches are so laden with fruit and have gotten so long in the 4 months that they are hanging on the ground.  Also, should I move the quince? I'm loath to do it as it just this year started fruiting, but I feel they are likely much too close to each other given the exuberance of the fig