A former colleague used to do Hudson to Eagan which wasn't too bad. (The worst part was crossing the river on 494, which you won't have to do.) However, once you hit the outskirts of St Paul/Mpls things will slow down considerably. You might have to swing north on 694 to avoid going thro St Paul which would be a long way around. Going into downtown St Paul and then north on 35E to Roseville and then into Mpls might be an option but that intersection in downtown is a killer.
Another option might be going thro Stillwater (over the liftbridge) and then on Hwy 36 but the liftbridge during rush hour can be pretty awful. It really depends on what time of day you're doing this. Have you considered moving to Stillwater or Bayport instead? That way at least you wouldn't have to try and get across the St Croix every day.