I am running into a bit of a brick wall. More like a stone wall actually. Some background.

I am in NY. biggest foothold trap we can run in water is 7-1/4" inside. 330's must be submerged. no snaring allowed. must be 15' from a hut, den or dam measured at water level. Can't shoot them.

I have a stream that is entirely large gravel. no silt and basically no eddies. Pretty good current and a rain is gonna raise the water a couple feet for a few days. Me and a buddy have been asked to come get some beavers for a friend on this stretch because of the chewing damage on his property.
I've found slides and actually a feeding landing just littered with small peeled sticks. Deepest water is mid thigh but most of the water is mid calf or lower. Almost no structure but the banks are anywhere from 5 to 20' and and so steep you can't just walk up them.

We have found the bank den on the opposite side of the stream (100' across). We can't get an H stands in becasue of the rock bottom. I can't find water that would be deep enough to drown.
I'm pretty handy fabricating but does anyone have any out of the box ideas for this (other than "find a new area"..lol)

Any way I can hold them on a foothold on land without a twist off/chew out?

If It were me I would set as shallow as I can and target a front foot. You want the beaver walking. And offset your trap about 4" left or right of center.
Set up a drowning cable, If you can't get a stake In at the deep end just use a heavy weight. A front foot caught beaver can be drowned In about 2' of water.
Can you wade Into the den site? If so just run a pole through each of the 330 spring eyes. Rotate the springs up ward to lock the trap In position. Place the this set up In front of the den entrance with the 2 poles above the water line and then drive a stake In to the bank and secure the poles to the bank.

When your done with the 2 poles the top end should look like the top of a teepee.

You would be better off keeping the caught beaver In the water then letting It get up on dry land. Have a little slack In your drowning cable that will act as a shock spring. And place a stop about 3' away from your deep end anchor. You don't want that beaver to be able to pull against anything solid.
A added weight like a window weight or a tie plate attached to your trap chain will tire out that beaver In no time.

Good luck.

KB stabilizer and pile rocks to neck the channel down some to where the trap has enough depth to be submerged about an inch or so. I did this in a spot last winter where I found open water in ledge and rock bottom. Piled the rocks up enough to lay a dive stick across the trap. My channel was only a few feet wide and rock was fairly blocky stuff easy to stack.

Why not just set a 330 submerged under a dive pole, and fenced on their approach to where they are cutting.Use a little castor on the bank to line them in.

Sure, footholds on drags or clogs like the Boss teaches.

Your landowner friend could also contact the NYSDEC and possibly receive a nuisance permit if beavers are damaging his/her property. Then you can remove beavers any way you want, trap, shoot, set on hut dam etc..

stiff sticks or stakes will hold 330's perpendicular to a steep bank as taught in Claudie Taylors Otter dvd....just below waterline.
A Sullivan Stabilizer holds the bottom to the bank wonderfully.

don't forget an MB coni bracket with a 1/4" spacer welded to any old steel plate works well for gravel bars/bottoms too

So what kind of a drag are you referring to ? It better not be wood since the beaver can drag It Into the water and float away with It.
And In my opinion if that beaver gets hung up In the stream side brush your asking for wring offs.

Does the 330 have to be fully submerged? If not then a float?

it has to be fully submerged. Picture this looking down the stream. 20 foot high bank on the left (so steep you cant climb it without grabbing trees. goes down to the water. The water from left to right goes from zero depth on a gradual slope for 90' to a depth of 12" Then it drops to mid thigh for 10'. The right bank goes up at the same steepness as the left but it varies in height from 5' to 20'. the bottom and low part of the banks is all large gravel. It's a trout stream with good current.

The float idea might actually work. I could anchor to the bank and use a weight into the middle. I would think the beaver would keep close to the deep bank to swim up stream since the flow is slower at a bank? . (their den is downstream from the cuttings).

Culvercreek, 330's actually don't need to be fully submerged. Just in the water is okay. I like 4 or 5 inches minimum. You need to camo them up with some light brush or grass pretty well. Don't want to educate them about square things. My son and I have used floats, they do work.

https://trapperman.com/forum/ubbthreads.php/topics/322065/Beaver_-_Beaver_Float_Pics#Post322065
Made one up about a week ago and got first one in a float this morning (no "camo" on it yet, just plain 2"X4"'s) as place along this "river" goes up and down daily. Nothing pretty but had waited too long doing it.

I am usually pretty good with regulations but totally missed that Thanks. That opens up some options.

You can set on a beaver dam if you have an open otter season.

I also think it is legal to set bank dens if you choose,not the same as a house,I would check with your local CO.

Just take a heavy peace of metal and weld a couple 40 penny nails to it that are bent in a v shape.Set 330 on it and you can lay the flat heavy metal anywhere you want in the creek.

Unfortunately we don't There isn't a dam present either.

They list "dens" specifically and CO says it's a no go.

We run into this same problem in our limestone bottom creeks.
We set legholds with long chains (8 feet) at crawl outs and slides we sometimes create ourselves. Stake em up solid on the bank a foot or so. Just be sure to set where there is nothing the chain can tangle on.
Beaver will be waiting on the bank or just lounging at the waters edge when you check em.
Dale Billingsley employed this method on big rivers in a video.
Works for us.

how heavy is the chain you run?