Thanks for getting in touch. I am not really much farther back on the Adsheads. I am still stuck with Thomas born either 1806 in Ashton under Lyne Lancs or 1811 in Northenden/ Macclesfield in Cheshire. In every census I can find he claims to have been born in Ashton in 1811 but there is no baptism in 1811 but I found one in 1806 in Ashton. The only baptisms I have found in 1811 are in Northenden & Macclesfield but if he came from either of those 2 places why say he was born in Ashton?
I am now in touch with another of his descendants but she is stuck with him too. Many of my other lines are going really well, others are stuck like this one.
At least it looks like you are making progress with yours! If you do find this is the right William hopefully you might be able to go back a bit more.