OK, you asked for suggestions. Here goes:
That's a nice project. BTW, & congratulations on getting 100+ years on the original.
Concrete box culverts are very nice, but spendy. But do that if you can afford it. Steel culvert is way less expensive, & 100 years is reasonable. Steel culvert quality varies a lot. Some of the better is heavier gauge and coated.
Just guessing based on our area, these 4 items listed below on a rural job, on a private road to private land could cost as little as $5K each or as much as twice that. Allow the same $5K for overruns and so you are at $25K. min. here. Not bad compared to $50K, and frankly the $50K you were originally estimated too far isn't out of line if this road sees tonnage or has to be rated in any special way - for fire trucks for example.
1. I would call around and see if I could get an older professional civil engineer on my side. His stamp will be needed, and he can design alternatives for some regulations. He has probably dozens of this type repair & has stream data and local knowledge.
2. Ask around to see if anyone sleeves old culverts. A 5 foot sleeving for existing 6 foot pipe can be considered a temporary internal diversion since it prevents the construction muck from being carried downstreanm - which from your photos is what is happening with the undermining going on right now. The civil engineer will need to draw up plans for the DEP so that the sleeving is an acceptable temporary bypass.
3. Expect to put in a pair of new six foot culverts - one on each side of the central sleeved pipe...or whatever fits. It's good practice to ALWAYS put in two or more same size culverts side by side - each one sized for full flow. Climate change means local flooding, so an even better idea is to have one or more offset above the others in case of flood debris plugging the lowers. This is the time to do this job because most local codes haven't changed as much as the climate will....yet.
4. Plan for a large excavator. Looks like a one day job but allow for two. The excavator should already have knowledge/permits for working around power lines.
Tell him he may need to do some compaction around and between culverts. He will know that anyway..
You could make back some of your cost if the culverts displace enough decent dirt to avoid having to bring in fill. But you won't know that until you dig.
5. Put the guard rails back to code.
Good luck,
rScotty