I think [MENTION=526881]Herzlos[/MENTION] has the best idea, take the lane for one mile and enjoy the rest of the ride.

Of the two choices OP laid out, the shoulder might be the better idea, although it depends on how well the shoulder is maintained. Lots of broken glass, ripped up beer cans, a few 2x4s with nails sticking out laying across the shoulder? Not ideal.

You say cut grass shoulder, I think grass concealing the broken glass and mowed can shards. Throw in a couple 3" wide rivulets about 4" deep that the mower smooths the grass over to make sure you can't see what lies underneath. Eh, while I'm climbing 600' I'll be going slow enough on the paved shoulder to avoid most of that.