I have seen other solutions to muskrats by laying down galvanized metal fencing along the shoreline and below, then rip-rap and small gravel on top of that to cover up the fencing and hold it down. I don't know how deep below the shoreline the little buggers will dig but you have to go at least that deep.
To help reduce their numbers, get rid of their favorite food: Cattails and other vegetation they like to eat. Also, a mink or two will do a fine job of emptying out muskrat dens.
For erosion control, the above post using natual erosion mats until the season is better for seeding some ground cover. No trees or you will regret it. Besides root penetration through the dam, they are also prone to consume water, and put leaves and needles into the water, thereby aging the pond faster.
Also muskrats love to tunnel among the tree roots, they cut the roots when they are digging and get a more stable home that way that is less prone to collapse.
They have a hard time understanding that they have to tunnel in from more than 24"-36" water depth. Beavers on the other hand have been known to start their run at more than 48" below the surface. I've gone over my chest waders when stepping in an unknown beaver run. Not a fun thing to do in November!!!