Karen,
In a very junior capacity, I wrote easements for an agency of the US government. For the uninitiated, an easement is not an easement is not an easement. An easement can be written to be squishy and meaningless, like a license acknowledging the other parties existence and protecting the servient estate's property rights. At the other end of the spectrum, an easement can be written to be iron clad to be equivalent to the fee simple estate. In this regard, the brief linked above said, "After reviewing the easement terms, the court declared that the overall structure of the grant, along with the specific enumerated rights of the easement. . . ." It is never good to draft a vague easement.
If I was in your shoes, the first thing I would do is meet in person the BLM realty specialists in your region, maps and deeds in hand with a signed letter from the other property owners (keep the crazies at home), and see if the BLM would be willing to relax or concede some rights. You might be surprised. I wouldn't rush to sue as it immediate puts all parties in an angry defensive mood -- Legal procedures are very particular and you are no longer able to have a human conversation.
If they are unwilling, then you are in the landlocked scenario and have to pursue the RON I've already elaborate. You might consider purchasing as a group the servient estate underlying the road as well to be able to control it.