Matt, Yea its pretty captivating work and sounds like you have already figured it out. make the water do the work. widen your hole all the way across. Just work back and forth. start on the opposite side and work towards the other. Anything the water does not remove, you have too. Don't let too much stick up because without water, it's just plain hard work
Trapping beavers is really easy like I said. If you have them in all the creeks and have already spotted were they are cutting now to feed you'll have no problem trapping them. Set your traps in the water where they won't freeze up in an obvious pathway. Use those pointed, de-barked beaver sticks to build a picket fence on either side of the trap. Just stick them in the mud and leave some sticking up for the beavers to see and they will swim between them right through the trap. Sometimes I lay one across the top og the trap to make them duck their head. Be sure and stake the traps down so nothing can drag them off. If you arn't saving hides, they'll keep in the water just like your refrigerator so every three or 4 days will be fine. Invest in the trap setter or just make your own. You'll be glad you did. The 330's can be a challenge at times to set and use the safety link but don't forget to unlatch it. All that will make sense when you see the traps.
With a river close by you'll probably have intermitant problems every couple years. There is probably only one family unit on the lake. The juveniles will usually strikout to find their own territory but there might be two groups on the lake. there could be as many as 6 in a single lodge, but usually only one dominant male and female. Walk the lake and look for lodge holes or brush lodges