Did you check for bridge tie strips from either Micro Engineering or Central Valley that are set up for gauntlet track?
Edit:
Central Valley makes them:
https://www.shop.cvmw.com/Gauntlet-HO-Code-83-70-ME-1907-8.htm
The ties will need to be wood so that the rails can be spiked down. If I'm using wood ties it seemed like using wood to hold the ties together would be easiest. I believe the stringers are what hold the ties together along with wood guard rails on a wood trestle.
Have you thought about using styrene for the bridge deck? I think it's an easier material to work with. The bridge deck itself will not show off the craftsmanship of wood working.
It takes an iron man to play with a toy iron horse.
The entrance to my "U" shaped layout will have a swing gate with a railroad bridge and gauntlet track which completes the inside double loop of track meeting at the bridge. I am currently working with three Atlas deck truss kits #84 and bridge piers #81 to make the bridge. The problem is the Atlas kit's plastic deck above the truss is not wide enough for the gauntlet rails and the plastic guard rails and rail cleats get in the way of two sets of track. I am considering constructing the entire deck from wood which will require a lot of work. Suggestions are very welcome.
Capt. Brigg Franklin; CEO Pacific Cascade Railway in HO gauge: