During my few years in upstate NY, I found that the famously grey weather around the Finger Lakes greatly helped my exposures inside covered bridges. Most have plenty of small openings, so strong daylight makes for a huge zonal range. The diffused light of a cloudy day greatly helped the effort. Not sure what time constraints you're under, or what the weather is like for you, but it is by far the cheapest and easiest way to minimize the problems. For bridges of that length, artificial lighting would be very difficult to utilize for even illumination without access to the span itself. Dusk or dawn would be a good second choice, especially if you can get a little fog to help the situation.

Probably nothing you don't already know.