I now have the two potential marriage certs in front of me.
The 1854 marriage to elizabeth chapman, has John Broad, a quarryman, son of William Broad, quarryman
The 1863 marriage to Mary Jane Thomas has John Broad Read (widower), labourer, son of William Read, labourer.
So I don't think that provides any help in linking them together.
However whilst the 1841 census has a few possible hits to choose from, running a search of ancestry with the terms John Broad Read born 1827-31 came up with just one good hit for 1851 and 1861, the family you had already identified. I have located them in 1841 and their son John is not at home, so could be any of the other 1841 hits.
I am becoming convinced that we are on the right track, but how do we explain the father's name on the certs being different? It would be very helpful to locate the marriage of William Broad (or Read!), born approx 1806 and Mary, born approx 1811, but so far I have had no luck.