There is no information available from Ezekiel Duty's manuscript on the Southern Branch in regards to the three brothers' parents. As you noted, it is believed the brothers ventured from Maryland and Virginia into N.C..
E. Z. even noted that some traditional stories are told of the brothers arriving directly from the British Isles. I know many as well as myself have researched your inquiry with no clear answers.
We do know the brothers were established in N.C. prior to the Revolutionary War.
Would you happen to live in Texas? I reside in Austin.