Regarding Francis R and his parents birthplace: All census seem to confirm F R was born in NH. The 1880 census says his father was born in NH and his mother in MA; this is a rare combination amongst the TIBBETTS with only one other showing in the 1880 census.
I am not related to this branch. My interest is my worldwide One Name Study on all T*BB*T(T)(S) families for which I hold many thousands of VR, Census and other records.
If we can get through your 'brick wall'by one more geneation, I can you back to 1500s very quickly.