re: Engineers of the OB: Will this bridge support a loaded log truck?

Should have started with this photo. Hard no for me. I'd say get an old railcart or go with a culvert and backfill. Probably some farmer/logger that will let you borrow a culvert to set and remove for a fair price.

If at any point the creek bed is dry or almost dry I would but in footings and piling every 6 foot for a permanent reinforcement. You could also build a series (8) of 12”X12x12 framing a for concrete footings then buy 8 screw jacks and 8 4x4s to support the structure. It’s a temporary and non permanent fix and easy work around instead of a culvert and permit. I’d place them all in the center with 4 splitting the couplings. Should increase the load bearing capability by 20,000lbs easy.