First question - if the beaver activity damages the road, will that affect access to the property that doesn't want to allow you to deal with it?  If so, that gives you a bargaining chip.  If not - oh well, it was an idea.

Maybe get in touch with Inland Fisheries and see if they have any suggestions?  How wide a right of way does the association have rights to?  Would a beaver deceiver be within the right of way bounds, and therefore within the association's rights?

Have you tried contacting Inland Fisheries to see if they have any suggestions?

Another possible source of help is USDA Natural Resources Conservation Service (NRCS).  They assist private landowners with issues with stream crossings.   I'll attach a brochure.

I've been trying to think if there are any statutes that might help you, and the closest I can come is the following: 

Title 17 §2802. Miscellaneous nuisances

The erection, continuance or use of any building or place for the exercise of a trade, employment or manufacture that, by noxious exhalations, offensive smells or other annoyances, becomes injurious and dangerous to the health, comfort or property of individuals or of the public; causing or permitting abandoned wells or tin mining shafts to remain unfilled or uncovered to the injury or prejudice of others; causing or suffering any offal, filth or noisome substance to collect or to remain in any place to the prejudice of others; obstructing or impeding, without legal authority, the passage of any navigable river, harbor or collection of water; corrupting or rendering unwholesome or impure the water of a river, stream, pond or aquifer; imprudent operation of a watercraft as defined in Title 12, section 13068-A, subsection 8; unlawfully diverting the water of a river, stream, pond or aquifer from its natural course or state to the injury or prejudice of others; and the obstructing or encumbering by fences, buildings or otherwise of highways, private ways, streets, alleys, commons, common landing places or burying grounds are nuisances within the limitations and exceptions mentioned. Any places where one or more old, discarded, worn-out or junked motor vehicles as defined in Title 29-A, section 101, subsection 42, or parts thereof, are gathered together, kept, deposited or allowed to accumulate, in such manner or in such location or situation either within or without the limits of any highway, as to be unsightly, detracting from the natural scenery or injurious to the comfort and happiness of individuals and the public, and injurious to property rights, are public nuisances.

https://legislature.maine.gov/legis/statutes/17/title17sec2802.html 

It's not an exact match for your situation, but the principle similar, that is, a person should not be able to do something that damages other people's access to their property.

I wonder what made the person object to the beaver deceiver, and/or if they were the ones who removed it.  Could it be replaced without going onto the person's land? 

I'm thinking it might be helpful to get a professional mediator involved to contact the person and listen to their concerns, and find out what caused them to have their current objections.  Are they nature lovers who don't want the beavers disturbed?  Or do they have a grudge against someone who needs the road for access?  Did someone trespass on their land?  There could be any number of things motivating them, and if you can find out what has them upset, perhaps something could be done to address their concerns first, and then resolve the issues with the road.  Such conversations can be delicate, which is why I would recommend getting a professional mediator rather than trying to do it yourself.  The Maine Association of Mediators has people with the skills to handle it.

Unfortunately I cannot tell you how much Mediation would cost.  It used to be possible to get a Mediator from Family and Community Mediation (FCM) at nominal cost, but unfortunately that organization no longer exists.  But many of the Mediators who had been involved in that effort are members of the Maine Association of Mediators, and might be willing to negotiate an affordable rate - I don't know that, I'm just speculating.  I believe most charge less per hour than an attorney, although the rate probably varies depending on who you hire.  Some offer a free preliminary interview.  The big saving is that your case will probably be settled a LOT sooner, both due to a more direct process, (i.e. no attorney hours spent researching related cases and preparing court filings,) and due to avoiding the court backlog.  

To find out more, go to the Maine Association of Mediators website, here: https://www.mainemediators.org/ 

I just ran across two more statutes that might be applicable in your situation.  

Title 14 §7551-B Trespass damages

1. Prohibition. A person who intentionally enters the land of another without permission and causes damage to property is liable to the owner in a civil action if the person:

A. Damages or throws down any fence, bar or gate; leaves a gate open; breaks glass; damages any road, drainage ditch, culvert, bridge, sign or paint marking; or does other damage to any structure on property not that person's own; or [PL 1995, c. 585, §1 (NEW).]

B. Throws, drops, deposits, discards, dumps or otherwise disposes of litter, as defined in Title 17, section 2263, subsection 2, in any manner or amount, on property not that person's own. [PL 1995, c. 585, §1 (NEW).]

[PL 1995, c. 585, §1 (NEW).]

2. Liability. If the damage to the property is caused intentionally, the person is liable to the owner for 2 times the owner's actual damages plus any additional costs recoverable under subsection 3, paragraphs B and C. If the damage to the property is not caused intentionally, the person is liable to the owner for the owner's actual damages plus any additional costs recoverable under subsection 3, paragraphs B and C.

[PL 1995, c. 585, §1 (NEW).]

3. Damages recoverable. The owner's damages include:

A. Actual damages, as measured by subsection 4; [PL 1995, c. 585, §1 (NEW).]

B. Costs the owner may incur if the damage results in a violation of any federal, state or local law or ordinance and, as a result, the owner becomes the subject of an enforcement proceeding. These costs include attorney's fees, costs and the value of the owner's time spent on involvement in the enforcement proceeding; and [PL 1995, c. 585, §1 (NEW).]

C. Reasonable attorney's fees for preparing the claim and bringing the court action under this section plus costs. [PL 1995, c. 585, §1 (NEW).]

[PL 1995, c. 585, §1 (NEW).]

4. Measure of damages. For damage to property under subsection 1, paragraph A, the owner's damages may be measured either by the replacement value of the damaged property or by the cost of repairing the damaged property. For damages for disposing of litter, the owner's damages include the direct costs associated with properly disposing of the litter, including obtaining permits, and the costs associated with any site remediation work undertaken as a result of the litter.

[PL 1995, c. 585, §1 (NEW).]

5. Other actions barred. A recovery from a defendant under this section bars an action to recover damages under section 7552 from that defendant for the same specific damage.

[PL 1995, c. 585, §1 (NEW).]

SECTION HISTORY

PL 1995, c. 585, §1 (NEW).

Here's a link to that statute:

https://legislature.maine.gov/legis/statutes/14/title14sec7551-B.html

The other one that might apply is this:

Title 17 §2808. Alteration of surface water flow

§2808. Alteration of surface water flow

Unreasonable use of land that results in altered flow of surface water that unreasonably injures another's land or that unreasonably interferes with the reasonable use of another's land is a nuisance. [PL 2005, c. 564, §1 (NEW); PL 2005, c. 564, §3 (AFF).]

An action under this section must be commenced within 3 years after the cause of action accrues. [PL 2005, c. 564, §1 (NEW); PL 2005, c. 564, §3 (AFF).]

SECTION HISTORY

PL 2005, c. 564, §1 (NEW). PL 2005, c. 564, §3 (AFF).

Here's a link to that one:

https://legislature.maine.gov/legis/statutes/17/title17sec2808.html