This may sound harsh, and I do think you have a valid complaint both on the "fairness" front and on the matter of how the association is being run. (In fact, you are not the first person on that road who has complained about unfair assessments. Someone wanted to put in a rental property, I believe, and the association figured they could get them to pay a huge proportion of the road maintenance cost. I never heard how that one turned out, but it does sound like the Association is looking to get someone else to foot the bill.) But there are other things that need to be considered, which may well make it unproductive to pursue trying to get your dues reduced.
You still are not correctly understanding what is meant by "appurtenant" in Hermansen's explanation. The easement to the lots beyond you is appurtenant to all of the lots to which it was granted. The reason you apparently can't use the rest of the road is not that the other lots are not appurtenant. The reason you can't use the rest of the road is that your deed only grants you an easement to the 50 foot right of way, not to the narrower right of way beyond. The 50 foot easement is appurtenant to your lot. The narrower easement apparently was not granted to you and therefore is not appurtenant to your lot.
As for the reason why length of road used is not generally a good way to determine each person's share, you would have to also figure in how many people use each section of road. So, say there are ten people who own land on a road, and each owns the same amount of frontage on the road. On your theory, if the owner of the tenth lot owed $100, then the owner of the first lot would only owe $10. The owner of the second lot would owe $20, the third $30, etc. But why should the owner of the tenth lot have to pay $100, when most of the wear and tear on the rest of the road is due to use by others? He should only have to pay 1/10 of the cost of maintaining the first section of road, because the other nine owners would also be paying to maintain that section. He would have to pay 2/10 of the cost of maintaining the second section of road, because eight other owners would be contributing. When it came to the last section of road, he would pay 100% of the cost.
Now that may look relatively simple to figure out, but how do you do the calculations for each owner when the lots are different sizes, so that each section of road each owner uses represents a different percentage of the length of the road? And do you also take into account whether each owner uses the road seasonally or year round? Or how many people in each home drive cars? Or whether they commute daily, or only go out a couple of times a week? Or how heavy each person's vehicle is? Or, (one of my pet peeves,) whether the person habitually drives in the same two ruts and insists on using it any way he pleases in mud season, or whether he rides the high spots to help even out wear on the road surface, and avoids using the road during mud season? I can make twenty trips out the road with my car, riding the high spots, and do less damage than our neighbor making two trips in the same two ruts with his pickup. It could get extremely complicated to try to figure each person's fair percentage of the cost of road maintenance.
Another factor to consider is the value that you are getting. It looks like the dues you are being asked to pay are comparable to what it would cost just for snow removal on the length of road you use. (The plow contractor on our road charges $250 to plow a 100 foot driveway for the season.) Yet presumably you get summer maintenance as well.
If you were to take the matter to court, you would probably get less than two hours of an attorney's time for what you are paying for your annual dues. Some types of cases in Maine are now required to attempt mediation before they go to trial. But I'm not sure what kinds of cases that applies to, and even if your case would qualify, you would likely have to hire an attorney in order to get to the point where mediation is required.
One option you may not have considered is that it appears your land has frontage on Webbs Mills Road. Given the tremendous cost of attorney fees for taking a case all the way to Court, it might cost you less to put in a driveway directly from Webbs Mills Road and build a stone wall all along Sloan's Cove road so you have NO access from Sloan's Cove, if that would get your road association to agree that you do not owe them dues. Not a very practical solution, I'm sure - but an illustration of the cost of Court action.
So while your current dues may not be as fair as you would like, I'm afraid I don't see an option that will save you money, unless you can appeal to your neighbors and try to get them to see it from your point of view.