I believe the first thing I would do, is see if you have enough fall to drain the water. Do you know anyone that have a level, or transit..?? A simple Lock Level, and folding rule, or tape measure will do the job. You'll need to see how far beyond the culvert you'll need to go, to let it to drain properly. 2% of fall is sufficient.
If it's a smooth bore pipe, they can be moved. You can straddle the pipe, clean off the top within an inch or so, then offset yourself enough to dig down past halfway of the pipe. You need to relieve the side presure at the widest point. It may take some handwork to get it fairly clean. When totally exposed, put chain around an end, and gently lift. If it is the bell type connection, it should pull apart, lifting up. Just be careful of the rubber gasket. When reassembling, use some spray on vegetable cooking spray as a lubricant. Take the hoe, and push back together gently. Use a solid object to buck against. Tree, post, etc.
Digging beside it, and letting it roll in lets material on the lower side fall in the hole, and not have a level bottom of the ditch. Twice as much work, trying to clean it up, with the pipe on top of it.
Also, remember you will be shooting grade for the invert (flow line) of the pipe, not the O.D. With a 16" pipe, I'm guessing 1 1/2" to 2" walls of the pipe, so you will need to go that much deeper where the pipe will lay.
Just guessing here, but where you live, I'm betting thye specified 67D, or 304 Limstone over the pipe. Should be fine for reusing, although if the pipe was just put in th ditch, then covered, you may get a lot of dirt mixed in with the clean limestone backfill. As mentioned be sure to tamp it back in in lifts. You'll have an extra wide hole to allow a plate tamper alongside the pipe.
Under highways, we put sand around the pipe, and covered about 1'. Then flooded them with LOTS of water. You'll get approx. 98% compaction when the water soaks out. then you can cover with limestone, and compact. Doubt they let you do that though... They wouldn't let me do that, just south of you in the next neighboring county....
All in all, if you don't have your own hoe, renting a steel plate, and other costs incurred, $600.00 isn't all that bad, by the time you figure it all up. And in the big picture, if it doesn't drain properly, it's the Townships baby...
