I think your geography is off. The Montana side of the Hiawatha goes into ID,
away from the eastern start of the CdA trail in Mullan.
I was just riding out there last year. From St. Regis I climbed Gold Pass (15 miles of dirt/gravel) to the ID border, then down to the St. Joe River to Avery (nice, paved road). From Avery, I road the former Milwaukee Road right-of-way for 9 miles to the Pearson Trailhead of the Hiawatha, which is the western end of that trail. Took that all the way to the East Portal Trailhead, which is in MT. From there, I went down the dirt road and picked up the NorPac Trail, which takes you back to the border with ID at Lookout Pass. From there, you can either take I-90 down 7 miles to Mulan to pick up the CdA or you can continue down the NorPac Trail to Mulan. I chose the former as I was sick of dirt at that point.
You can see what I describe above here between mile 74 and 172.6:
https://ridewithgps.com/routes/29428535Ignore all those profile spikes on the Hiawatha. That's GPS data coming from the tops of the dozen or so tunnels on the trail.
If you want to experience the Hiawatha and all of the CdA and even more trail you could do:
1. Do what I did above to St. Regis
2. Pick up the Olympian Trail in St. Regis, which become the Hiawatha Trail at the East Portal Traihead. (They are both on the same former Milwaukee Road right-of-way.
3. Ride the Hiawatha to its western terminus at Pearson
4. Catch the shuttle back to the west side of the St. Paul Pass Tunnel on the Hiawatha and ride back through the tunnel to the East Portal Trailhead.
5. Do what I did from East Portal to Mullan.
Don't expect nicely groomed surfaces on all parts of the Olympian and NorPac Trails.