You will have no problem using MS Rd. However they will have guys on horses running the fence lines trying to catch people sneaking in (typically on the east, north, and south sides of Mountain Island).
I had a different problem in the 90's with Escalante Cattle Company blocking roads and marking public as private. We even had actually went so far as having to draw our pistols one day (very hairy situation). Now they are under different mangement and we have not had anymore problems.