can I travel overland from Dunhuang to Lhasa in my own vehicle? I have unlimited chinese residence permit

Obviously the critical point is the border crossing into the province of Tibet. When I obtained the residency card I was told I enjoy all benefits of Chinese citizens except voting - so I would expect that travel restrictions to foreigners don't apply to me. During my travels I experienced often that even officals at check points don't know what the residency permit entitles me to.
How can I make sure in advance the border officials let me cross into Tibet?