What I'm tempted to do is to go west from Gays Mill then North again on 35 to LaCrosse then back over to MN to check out that interesting looking little loop in the SE corner of the state that is made up of highways 16 and 44 then head down the river road to Dubuque on the IA side.Of course maps can be deceiving so if you have knowledge of that section of MN or 35 between Gays Mill and LCrosse let me know.
I'd say that would be a good plan. 16 is a Byway -
Historic Bluff Country Scenic Byway. Lanesboro on 16 is a really cool town, there is a lot of canoeing, rafting and peddle biking going on. You won't be disappointed with that road. I've never been on 44 but thought the same thing you did from the map, even if it isn't that great it still looks like the best way back from when 16 straitens out.
The section of 35 south of La Crosse is Blah,
Consider this route back up to La Crosse.
Let me know what you think of 44 if you end up going that way.