One thing that may help these situations would be an increase in the number of beaver trapping permits that are issued each year. NJ issues only 200 permits each year across the entire State, for a season that only lasts for 5 weeks. I was lucky enough to draw a permit this year along with an otter permit. There is really no good explanation for it. I follow an Iowa trapper on YouTube and their season is very long and there are no permits required and no bag limits.
Here is a good example of the restrictions. Well Mills is in Beaver Zone 11 which is 333,000 acres in size. Only 6 permits per year are issued. I live in Zone 10 which is 88,000 acres in size and there are 8 permits issued.
My gun club is having a huge problem right now with our lake and dam and we are SOL until next beaver season. For the last 3 years, three of us trappers applied for that Zone and no one was successful. We tried for a damage permit but because we haven't flooded out the traffic on the adjoining county road yet we don't qualify.
Here is a clip from the NJ Interactive Beaver Map and a clip from the annual regs showing permits available. Bear in mind that the number of licensed trappers in NJ is only around 1,200 right now and has grown in the last few years. When I got my license there were only 600 trappers. 200 permits Statewide seems ridiculous.