I originally, based on Turton, had William b. 947, d. 1037, and having children by his 990 marriage to Emma, who were born in 1015. This seems like a lot for a 68 year old man.
It turns out that the person born c 947 was Raymond who m. Adelaide (not Arsinde her sister), and had William III who m. Emma.
The way I have Raymond's parentage is the simplest. There is an alternative being debated, which has Raymond as son of Raymond, son of Raymond, son of Ermengaud Vicomte de Rouergue, b. c 860, who I have as his great great uncle (Raymond II's younger brother).