Many of these places offer lake-run rainbows, similar in spirit to steelhead. They're not Olympic Peninsula winter fish or Idaho B-runs, but they are fantastic salmonids considering they don't get to plump up on ocean protein. For most intents and purposes, they are junior steelhead.
Historically, the closest steelhead ever came to Montana was up the headwater forks of Idaho's Kelly Creek (which go basically to the state border on the Continental Divide), but that ended when the North Fork of the Clearwater River was dammed in 1973. Today, the closest that steelhead come to the Big Sky is in the Salmon River, which is about 8 miles (as the crow flies) from the border, in the Beaverhead Mountains. (Correct me if I'm wrong about any of this - it's all from memory and I'm finding the information hard to track down).
Swinging flies can remain the preferred technique for hooking these trout, but if you love the rarity of catching a winter steelhead on a swung fly, you might consider other tactics that offer the challenge and exclusivity, like committing to the mouse (on any given Montana fishery). It's similar in that you're likely fishing for big fish, and you really need to spend time searching for "players". If the tug is the drug, the slam can be your jam (*please withhold feedback on that one). And if you're really bored with trout fishing, you can fish a mouse in any of the few-but-big fisheries mentioned above.
While you're not going to catch the mystical, giant, sea-running oncorhynchus, you're also not putting pressure on this vulnerable and important species, joining the masses sprinting to this latest greatest trend in fly fishing (this jab is not aimed at all who pursue them). And you can save a little money, lighten your carbon footprint, and anger your significant other a little less.
I too yearn to catch steelhead, but in the mean time, I can challenge myself in Montana.