There are two structures west of this bridge that have the old style MSHD guardrails - one is striped for a single lane and the other is wider than the roadway by a couple feet on each side.
They look like bridges in Google Maps which has some new high resolution imagery of the area and judging by the guardrail style they would have been built around the same time as the rest of this highway (mid 20's to early 30's).
uglybridges.com has listings for some possible suspects but the coordinates are screwed up for several - it's showing them as way outside of Cooper county.
I'll try to get a couple of pictures next time I drive by.