I come not to give help, but maybe to give hope!
I'm going to retell a tale I told elsewhere here recently, about how I discovered who my gr-grfather really was. He came from Cornwall and he was born around 1850 ... but you can't have him.
I'd be sure that your fellow's Kempthorne name came from somewhere other than his birth certificate. There are certain common possibilities, of two varieties:
- mother was not married, he was registered under her name
- mother was married, he was registered under her husband's surname
In either case, father was actually a Kempthorne and knowing this, he adopted his surname
- mother (re)married or partnered with someone, he adopted stepfather's surname
- he changed his name as an adult to avoid something: military desertion, debts, wife and kids, ...
(this, I learned from the son of my mum's cousin who knew but had no idea his name was fake, long after I figured out who he really was, was the case for my gr-grfather: abandoned the military in India after 5 years rather than be sent to Afghanistan, which fit precisely between his first identity's wife's death in 1873 and the beginning of the Anglo-Afghan war in 1878.)
People generally did not stray too far from their truth (as my gr-grfather's tale shows), so things like given name, age and reported place of birth are likely to be fairly reliable. Unfortunately, your fellow was a John. Mine had the good grace to have two multisyllabic trendy Victorian names.
Anyhow, herewith my tale (in very abridged form, since it took years to collect all the bits of substantiating evidence, and I've omitted most of it here). And after all this, I still don't know where his fake surname came from!! But I will figure it out or die trying.
I'm going to take a poke at your John, since I've made a bit of a specialty of name-shifters, being a self-taught expert after cutting my teeth on those people! Oh, and my own fun bit is that I finally bit the bullet and went for YDNA testing, and while I didn't expect a match with the rare fake surname, I did expect one with the common as dirt real surname, if my man was really a son of his official father. I got a match alright, a very close one ... with a completely different surname from the same area of Cornwall. And the search resumes ...
But if you have a male-line descendant from your John, you should consider YDNA testing. I was enormously lucky that one person from the well-researched clan in question, with whom my gr-grfather's descendant matches, had done the testing; otherwise I'd be none the wiser. Possibly even a Family Finder test, if you don't have a direct male-line descendant, would produce some ideas.
So ... I discovered, immediately upon first researching him, that my gr-grfather did not exist before his 1883 marriage; he had sprung from nowhere, with two distinctive given names and very unusual surname. I did not know where he was born, but I knew his (approx) year of birth.
Unfortunately for me, we knew that after he married in England 1883, he was in Australia for the 1891 English census, and I could not find him in 1901 for love nor money, to at least find what age and place of birth he gave. He then immigrated here to Canada.
Let's say their names were, for illustration:
My gr-grfather Edward Arthur Moonwalk.
His daughter Alice London Moonwalk.
His father Fiscus Moonwalk.
I got an early clue: when searching for the birth of a daughter of his that we had just learned died in infancy, Alice Moonwalk, I found that she was Alice London Moonwalk -- and I found the marriage of a person a generation before with the identical name, otherwise unique in recorded history. No idea how they were related, but they had to be. And when I searched for someone with the same given names as my gr-grfather born around the same time, I found an Edward Arthur Smith, let's say (the surname was nearly as common!).
Eventually, I found the family that matched all these clues, in the 1861 census (plus certificates): Edward Arthur Smith, with a sister named Alice London Smith and a father named Fiscus Smith. Born in Cornwall. And when I finally found my gr-parents in London in 1901 (his surname bizarrely mistranscribed at two different sites), he gave the same place in Cornwall, for his place of birth. So both he and his sister (that we had never heard of) had adopted the same fake surname, and both had assigned it to their father when they married, while retaining the father's real given name. Oh, the clincher was when I finally found that the sister's real name at birth was actually Alice London Moonwalk Smith. Why Moonwalk -- and especially how she came to have Moonwalk as a middle name -- I have yet to find out.
A big stroke of luck I had, when it comes to people changing names, was that theirs were distinctive and they retained enough of them, and their birth details, to make them identifiable. And while the little info I did have to start with was even less than you have -- his given names and approx date of birth -- finding the sister gave me a triangulation point you don't have.
Like me, you are looking for someone who
looks like your person. And then you see whether that person can't be accounted for after a certain point, the point where that person hypothetically became your person. And sadly, all the work you have done in that process has served only to eliminate the possibles ... but where there's life ... !