Wow, that's a sticky one.  It may be interesting to see what the result is due to the landowner covering the culvert with gravel.  The water will have to go someplace.  Will it then wash out the road, or will even more of it end up in the landowner's basement?

One thing that comes to mind is the provision in 23 MRS 3101 subsection 5-A.  Easements.  "A road association under this subchapter may negotiate an easement for the installation of a ditch, drain, culvert or other storm water management infrastructure to benefit the private road, private way or bridge. The easement must specify when a ditch, drain, culvert or other storm water management infrastructure must be maintained and include reasonable performance standards to guide the timing and extent of its upkeep and repair. The easement must also be recorded at the registry of deeds in the county in which the property subject to the easement is located. A ditch, drain, culvert or other storm water management infrastructure subject to an easement under this subsection must be under the control of and maintained by the road association."  

I am assuming from your letter that you have not yet obtained such an easement, and it doesn't sound like the landowner would agree to one.  Perhaps if you had gotten one before doing the work, you would have had more recourse.  At this point, your best bet might be to hire a professional mediator to help you and the landowner reconcile your differences.  Try Family and Community Mediation (FCM) or the Maine Association of Mediators (MAM) and see what they have to offer.