Unfortunately this is a fairly common problem.  I know of a number of cases where a private road or a discontinued road with a remaining public easement is used by the public to reach public land.  In the case of discontinued roads with public easements, there may not even be any public land involved, yet the public balks at the suggestion of converting it to a private road because they want the public to have access for hunting, fishing, hiking, snowmobiling, etc. 

I don't know of any where the Town has agreed to contribute to road maintenance.  The result is that private citizens are unfairly required to maintain a road for public use at private expense - which (in my inexpert opinion) should be deemed an unconstitutional taking of private property for public use without due process or just compensation.  I don't know of any such case that has been taken to court, although I know one where they were considering it.  I have not heard what the outcome was in that situation.

I was thinking the land in question was owned by the Town, in which case it would be unlikely to get the Town to contribute anything to road maintenance.  A Land Trust is a bit different, and I should have realized that from your original question.

The language of the deed does seem to imply that the general public will have free use of the road, which hardly seems fair if the other land owners are bearing the cost.  It may be possible to put some restrictions on the use of the road, but probably not to restrict the number of vehicles that can use it to reach any one property.

If it was always a private road, do the deeds to the various properties say anything about maintenance of the road?  If the road was laid out as part of a subdivision, often the deeds require that those who purchase the lots will become members of a road association to provide maintenance of the road.  If that were the case, the Land Trust should be no different from any other land owner - they should have to contribute to the cost of road maintenance.  Then the difficult part would be trying to determine what would be their fair share.  Where the owners of a residence might go in and out the road a couple of times per day on average, would visitors to the Land Trust land be one or two a week, or dozens per day?  (If the road was not laid out as part of a subdivision, it's unlikely that the deeds include such a clause, so that would be no help. )

Is there a formal road association on the road, or is it just an informal sharing of the costs of maintenance?  If the latter, you might want to consider forming a statutory road association under 23 MRS 3101-3104.  That would require the Land Trust as an owner of "benefitted property" to be a member of the road association.  The statute requires that the formula for determining each owner's share of the maintenance cost must be "fair and equitable."  While many road associations see the fairest method to be having each owner pay the same amount, in this case I would think it would be fair to base the fee on each member's estimated usage of the road.

How recently did the Land Trust acquire the land?  I'm assuming this is "non-residential" land.  In 2017, Legislation was passed (amended in 2019) requiring a disclosure in the sale of non-residential property if the access to that land is not maintained by the public.  See Title 33 section 193, here:  https://legislature.maine.gov/statutes/33/title33sec193.html  Paragraphs 1 and 2 were repealed and replaced with paragraph 3 in 2019, but depending on the date of the sale, one version or the other may apply.  That is, if the Land Trust purchased the property since the effective date of this legislation, the seller should have put the buyer on notice that the road is not maintained by the public, and (if after the revised version) should have informed the buyer who is responsible for maintenance of the road.  That would include telling the buyer if they are to be responsible for a share of the maintenance cost.

That's good that the Land Trust does contribute something, but the issue here would be what is "fair and equitable."  It doesn't sound like the previous owner of the land trust land, who granted the road to the subdivision, intended his "heirs and successors" to include the general public.

The difficult part will be trying to determine the Land Trust's fair share of the maintenance cost.  Have you discussed the problem with the Land Trust to see what their thoughts are? 

I wonder if there is some way to ask visitors to make a donation towards road maintenance, or at least get them to sign in so you can get some sense of how many people use it.  Maybe put in a trail camera on the road so you can record and count vehicles?  I'm not sure what the law is on that.