I echo Roger W's sentiment. Landowners who 'own' mountains, acceess thereto, or other interesting natural features, have to certainly expect that they'll be approached for access. If they don't want the hassle then they should not have bought the land. Or, they can set up a reasonable access program that benefits them as well as the climbers both.
The previous owner of the lands surrounding Culebra Peak seemed to me, IMO, to make access a big headache not only for interested hikers but for himself as well. Plenty of other mountains have access that cross private property where both parties have come to some sort of plan, usually through easements or something as simple as asking for permission first. Landowner fears of hikers 'falling into mines' or other somesuch I think are a smokescreen. Draft a waiver absolving the landowner of any responsibility and move forward. It's been done and there are plenty of good models in place that can be followed.
I am curious if the landowners actually live on the land and actively work it as a livelihood, or if they are located apart from the land and simply own it as property.
Not that I officially condone this sort of thing... but park somewhere hidden, get an early start and lay low. The mountaintop will be yours. Theoretically