If you MUST avoid the bridges (as I said earlier, I-10 is not like the old 2-lane causeway), you could go to Baton Rogue and then come down around the West side of the lake. Probably somewhere around Beau Bridge.
That is the "Plantation Road" along the West/South side of the river. Lots of history there.
We were last there the week before Christmas. We go every year for our anniversary. Unfortunately, this time my wife (stone sober) tripped on a bad place in the pavement of one of the little side streets off Magazine; fell and broke her left arm just below the shoulder. As of today Physical Rehab continues. We will be back next year, if not sooner.