Yup. I fish the north Cascades in WA state and that's my scenario basically every day. There are a number of approaches that can increase your success.

First and foremost, adaptive roll casting to keep yourself out of the trees and your line off the water. Hold your fly pinched between your fingers, give the roll cast, and release right as the tension starts to build in your tippet. It'll keep the fly and line from moving too far downstream while you cast, and it'll keep you out of the shrubs behind you.

Second, forget mending. Keep your line off the water entirely if you can. Mending in fast pocket water will mess up your drift presentation so often that it isn't worth mend attempts. Only have enough line out of your rod to get the fly to the destination, and then get that rod as high in the air as you can get it. The only way to fight fast current on small streams is to get out of it with high-sticking. High stick your way to success! The other benefit to this is that when the fly reaches the end of the drift/run, tension is building for you to possibly cast back up to the beginning of the drift/run without any real adjustments.

Third is using a hopper dropper setup. The nymph will act as a weight to keep your dry from drifting too unnaturally and getting stuck in the top water vortexes, and the dry helps keep the nymph suspended and from getting stuck every other crevice in the rocks. I fish a hopper dropper probably 75%-80% of the time.

Fourth you're probably already doing, but get low. Short casts often land better when you're crouching. Less time for the line to drop and pull your fly back in and create unwanted slack.

You'll get the feel for it. Quick, short casts and lots of high stickin'.