I can't believe I'm suggesting this, but didn't 105 5800 have a triple front DR version? Or was this the previous 10 speed 105's? Since I've been up and down the Maine coastline several times sailing, I know there are some pretty long climbs and maybe a triple would be a better way to adapt the current bike if there isn't room for a new bike.
Of course a triple might be more severe with noise cross chaining. Hopefully those will only be gears needed briefly. Also, the shifer will be an added cost along with other changes.
And in case I missed it, I'm still not certain the OP's bike is 11 on the rear, so I may just be prattling nonsensical stuff. Please don't tell me I always do that...... <grin>