When Elliotsville Plantation made the strategic shift from a National Park to National Monument it did get rid of some but not all of the short term major objections, unfortunately most parties agree that this is backdoor method of getting a National Park designation, therefore opposing groups feel they need to keep the NP issues on the forefront. I personally feel that its her land and she can do what she wants with it within the bounds of state law which are pretty minimal for an unorganized territory. Unlike a NP, the federal government only gains control over the donated land and only have the rights that EP had. There could be issues of existing legal rights of inholders and other neighboring land owners who have established rights to access their land over the proposed NM roads. I expect that part of the NM effort up front would be to either establish those rights formally or negotiate them away. In this case, there is always the opportunity for donors to buy more land and add it to the NM but the tactic of "starving out" inholders by denying either direct or economic access to their land is far less likely.
A proposed NP designation is different, it established a declaration boundary that covered significant private lands in the region. Inside the declaration boundary, the NPS becomes a major participant in what goes on even on private lands. The best nearby example is private land inside the ADKs where the park commission has significant input over activities on private lands. In many cases, NPS has expanded its reach outside park boundaries under the guise that changes to private land outside the park has an impact inside the park. From a national perspective that sounds reasonable but on a regional perspective where private landowners and residents are impacted its lot harder to justify.