Good luck with it all, sorry there've been no instant magic wands so far
With regard to the baptism in Hartford, Huntingdon, I think you can take it as a very strong possibility based on not just the fact that the year and details fit Joseph himself, but because of the use of Rosanna for one of his sisters, and he and Caroline then using it for one of their daughters. Hartford is not a huge place, and it would be a massive co-incidence if there was no link at all, though they might be families of brothers with the two Josephs cousins?
In the 1841 census Thomas is listed as 45, but that is the 'rounding' census. So is his wife, who is listed as Hannah. That's worth bearing in mind as Hannah and Ann can be interchangeable so any records could use either. Rosannah is at home age 13 so it is the same family, and Thomas is a Gardener. Thomas and Hannah were both born in county.
In the 1851 there seem to be just the two of them, and this time Hannah has been transcribed as Hannes. Their ages are given as both being 58, which would give them a birth date around 1793. Hannah's birthplace is listed as Stirtloe, which I think is near St Neots, but Thomas's as Distington, or that's the transcription, and that defeats me because it definitely says Distington, Huntingdon, but the only one I can find is in Cumbria. I've had a look at the original image, and I think it actually reads Dodington, which would make more sense. You need some local expertise on that.
Added: the 1861 is more clear - Diddington in Huntingdonshire for Thomas, and Stirtloe (Buckden) for Hannah. No luck on my hopes that grandchildren might visit from London and provide you with a link! In 1861 Thomas has decided to go up in the world and lists himself as a Greengrocer and they both give their birth as 63, not 68, so their birth records could be anywhere between 1793 and 1798,
Sadly for Thomas by 1871 he is 'inmate pauper' still consistently giving Diddington as his birthplace. There are a lot of inmates and some 4 pages back it gives the address for the first time as 'Carter's Yard' in Huntingdon but it has to be the workhouse or similar, though the word is not shown.
