A 4 mile detour isn't too bad, especially considering the low volumes. They will be delayed almost as long by the signal. In your next public meeting, tell the community it will take two years if you keep a lane open, or one with the detour.
Or, how about just detouring trucks?
In my NY State DOT days, we were redecking a bridge on a curve. The bridge designer said a 10' lane was plenty. The construction group said, no, it's on a curve, and the trucks will need more width because the back left wheel will off-track. They called us (Traffic Engr. & Safety) in to cast the deciding vote. I said get some flaggers out there, put cones where the barriers will be and see what happens.
Maintenance ran one of their snowplows through with no problem, but an interstate semi (19 m whgeelbase) came through and squashed a few cones. We put in a truck detour, but left the bridge open to passenger car traffic.