Actually, Snoqualmie Pass is I-90. Maybe you meant to say, Stevens Pass which is Hwy 2?
Tough call. Yes, both the Crowsnest (hwy3) and the North Cascades (hwy20) highways will have steep climbs and several summits/passes to negotiate. Using hwy2, Stevens Pass, will be the easiest climb of the three and a good road but, as you point out, it's adding more miles.
However, in my opinion, I'd use the Crowsnest as I consider it to be the better road compared to hwy20/North Cascades. It has lots of passing lanes and several places that will be 4-lane roadway. It's also the shortest route.
But I don't know your rig as you do. If you're worried about overheating, etc. because you'll be towing and loaded down to the maximum, I may even consider going to Snoqualmie Pass (I-90). It will really add a lot of miles but will be the gentlest grade and the best roadway as it is a 4-lane interstate completely.
But, Hwy2 over Stevens pass may be the best compromise.
Ack, I'm not being much help here, am I? I'll let others chime in on this one! Good luck.