Lowell,

FWIW, was an interesting show on Discovery?? last night. Sorry this is so vague, but, as I understand it, essentially beavers dam the culverts coming under rural roads. As they apparently work perpendicularly to the water flow, wildlife folks have created a beaver confuser that is a cage irregular in shape that causes beavers to give up the idea of damming the flow at the outlet. Might apply to your problem in a more permanent way than picking off the odd beaver...

Regards, Tim