I've heard Guinea fowl are even better at eating bugs than chickens. Maybe you could consider them for just the season and then sell them once the bugs are gone? They dont lay toooo much, and they are fairly low maintenance (from what I've read and heard), so they could be a good answer for your bug problem. You can sell any eggs you find (I hear its tough to get free ranged guienas to lay in boxes, but I could be wrong), or you can just let them brood chicks, which you can also sell (once ya catch em!). They like to roost in trees, so ya dont HAVE to use your coop space, and they are fairly safe from ground predators in the trees. IDK, just thought Id toss that out there- I know Id get at least a dozen if I was having that kind of bug issue. Something to think about....
As for chickens, you need, oh, at least 30 or 40, or maybe more, but, I LOVE my chooks and can never have enough, so my estimate may be tad high! 
By the way, you can always boil any extra eggs and then mash them up, shells and all, and feed them right back to your chickens if too many eggs is a concern.