Thanks for the message,
I am descended from William Watkins, my gggrandfather (born 1825 Chepstow, died 1871 Chepstow), he was an older brother of Alfred (b1836).
1851 and 1861 Cenuses say that David Watkins was born Ludlow Shropshire but like you I have been unable to find anything to confirm this.
You probably already know much of this, he married Caroline Smart in Clifton Bristol, 22 Feb 1819, and is shown as Davy Watkins, Source of this is Collection:St Andrew; Date Range:1777- 1839; Film Number:1595528 (this Ancestry found for me but no more information than this).
Apparently it was common for people to boat from Chepstow to Bristol to marry, a romantic day out...
I imagine there would have been witnesses to this marriage which just might be family members, maybe from Ludlow. However I haven't pursued this at the moment.
A few things come into my mind, perhaps his baptised name was not David? Also if he did travel from Ludlow to Chepstow, perhaps other 'Watkins' came with him.
Have you had any luck with the 'Smart' family?