I worked on a township bridge, mail ordered from the Milwuakee Bridge & Iron Co. in 1864 (No, I wasn't around then)that had a wood deck with many layers of asphalt paveing. Back then the bridges were sent out "tinker toy" style on a train or horse drawn wagons and erected on the site.
The township wanted to preserve the wrought iron truss, but was concerned about the weight limit. So, we ended up putting a new steel grid deck on the bridge, it was half the weight of the timber and ashpalt. That might be a solution for you to think about.
One thing to keep in mind, steel grid decks can be pretty slippery in the rain or snow, so post a low speed limit for the bridge.