For the females, it's definitely fighting a flood with a bucket, but it's better than doing nothing.

If you grab a bucket of males and a little hand tool that expands and retract to quickly rubber band their balls you could probably knock out up to 90 an hour on average if you spend 40s prepping a new band and strapping it on each mouse, but it's less effective because only 1 male is enough to copulate with many females, but at least it robs food from viable males and females. This might be really optimistic though, theres a chance the mice could gnaw the band off. EDIT: a hot iron clamp would probably work better...

If you know of a more effective approach feel free to present it, but clearly the poison tactic isn't going to work when they've already established themselves and reached this number.