wbuffetjr
With respect to WAE spawning, our (Colorado) Parks and Wildlife Department has been netting and removing fertile WAE here on the West Slope of Colorado and releasing sterile WAE. The intent is to reduce the risk of WAE escaping reservoirs, reproducing in the Colorado River tributaries, and predating several species of native fishes.

An example I can give is our McPhee and Narraguinnep Reservoirs here in southwest Colorado. McPhee is and impoundment of the Dolores River; Narraguinnep is in the San Juan River drainage. Both of these rivers are in the Colorado system.

I have no idea if sterile (possible triploid?) walleye are commercially available in this state. If they are, and you chose to stock a few, then at least they would not increase in number in your high mountain trout lake. It could be that a small number of sterile WAE would be a useful tool to limit brook trout recruitment, if that were ever to become an issue for you.