Since Richard Groves changed to & Son in 1817 and & Sons in 1822 we can assume that the sons (Thomas & William) were separated by 5 years. Can we assume that the firstborn might be given a second name as of his father, i.e William was born first? In the early 1800's ( according to Rabone history by 'Hallam'
an '& Son' could be used when the son was as young as 13 yrs old.
So William Richard Groves could have been born around 1804. So he could have been the William Groves listed in Whites in 1833 sawmaker. We could go on, it is mind-boggling to track a family history when succeeding generations always seemed to use the same name!
I agree with you that the 'wordier' the back the later the saw, so you could be right about later than 1850 ( Damn it!)
And now for some pictures ( maybe)