This can be done, but it will take a lot of work.
First, don't use stone for the base.
Do a 3"-4" footer with re-bar for the base. Then either set the block in the wet concrete, or use a good mortar to set the first course.
Do lots of measuring to makes sure you get the block under the culvert correctly without much fussing.
Be prepared to make lots of cuts also.
Now, personally in this situation the width of the road is a hindrance. The first time a plow or vehicle gets off just a shade, then the wall will take the abuse.
Here is a pick of something I did personally a couple of years ago. All done with concrete and mortar.
2 years later and there is still no movement.