Hi Sarah, and thanks for the post.
Firstly, I don't (yet) think there's a link between the Clews family that I'm researching, and yours. All 'my' Clews were involved in the ceramics trade - either working in the potteries, or actually as manufacturers. However, there's no reason why there couldn't be a link somewhere, as Stoke was at the heart of the waterways revolution in the 18th century, and I have found references to Clews as boatmen in cuttings from the Staffordshire Sentinel. Try a search on the British Newspaper Archive. The search alone costs nothing and can often be enough.
As for the spelling, this varies enormously. The Census returns from 1841 through to 1901 were filled out by the collecting officers, mainly because most of the population at that time was illiterate, and couldn't be expected to complete the forms themselves. Only since the 1911 census have householders been expected to do the form-filling themselves. This has meant a significant variation in spelling for unusual surnames, and Clews qualifies.
I have certainly found the same person with the surname spelled differently at different census periods. Clews seems to have been widely adopted by the late 19th century, but Clewes was very common in earlier periods, and Clowes also. I've found it necessary to search for all three, and found one return for a Clews where the spelling was Clays. If the person had a strong regional accent, then the census officer had to guess!
Not sure if that's much of a help!