In very soft bottoms, a single truck rotor (like a rotor from a one ton or bigger) will suck down and hold most beaver under. I can toss one 20 feet or so. If you must set these flat shallow areas, and you can get to knee deep water 16 feet out, set it up with the drowner and try for a front foot. If you get the front foot it will work, and with a good back foot hold it is not going anywhere. Personally I would use a full size beaver foothold of your choice, because if you get a front foot it is a drowning set, and if a back foot you want a big trap for the best chance of a good hold.
You will have to check daily though. If you cant check daily, those spots are about done when they get wise to BGs and you cant use snares. Move to another lake. Assuming you are fur or hobby trapping.
Now if these are nuisance beavers, first of all I would have a serious discussion about the consequences of limiting my equipment by not allowing snares. Consequences like me not taking the job. I dont recall ever having a landowner do that if the beavers were actually a big enough problem to throw money at them and call me. I show up with every tool allowed by law including a tritium dotted shotgun.
Just how big of a man are you??? I hope you played college ball and have dang good excuse why they aren’t watching you on Sundays!!
I’ve used truck rotors for coon drags and if you’re chunking them 20ft, you are the MAN!! I even used one for a coyote and he didn’t budge it.