Looking for "joseph rogers" just in UK / England / Norfolk in the 1700's produces a lot of results (some may be on different pages/images in the same document). This is also because Norfolk records on FS are mainly open to view at home.
https://www.familysearch.org/en/search/full-text/results?count=20&q.fullName=%22joseph%20rogers%22&c.recordYear1=on&f.recordYear0=1700&c.recordPlace1=on&f.recordPlace0=9&c.recordPlace2=on&f.recordPlace1=9%2CEngland&c.recordPlace3=on&f.recordPlace2=9%2CEngland%2CNorfolk
I spent the weekend wading through each and every document extracting any information regarding Joseph's whereabouts. A quick summary:
1725 - birth - unknown, born most probably in Norfolk († in 1806 aged 81 = 1725)
1750 - Heigham, Norfolk (marriage to Elizabeth Rippingale)
1750 - 1774 - Norfolk
1775 - Knapton, Norfolk
1776 - Swaffield, Norfolk
1777 (sept) - Swaffield, Norfolk
1777 (nov) - Kidwelly, Carmathan

1784 - London (marriage to Susanna Ingram)
1786 - 1795 - Pinner, Middlesex
1806 - Swaffham, Norfolk (place of death, aged)
His eldest son, Harmer Rogers of Woodbridge, Essex, is mentioned between 1793 and 1795.
By stating that Harmer is Josephs eldest son implies one or more other sons,,,,,,,

The mention of hometown being Kidwelly in the county of Carmathan, came as a suprise

Anyway, the timeline grows
