The answers to your questions are:
- Yes, the shift was and continues to be a gradual and chaotic process.
- No, there was not a a deliberate and possibly collective decision taken by the educational institutions, the media, or the government of the time.
Yes, there were a few changes that Webster tried, but the history of English spelling is much, much, much more complicated than that. English has never had a single agreed-upon spelling, even within any one country. There is no such thing as the American spelling, nor for that matter is there the British spelling, when discussing the English language. At most, there are individual words that may show a general predilection, but that shifts over time and within writers and publishers. It isn’t a simple us-vs-them situation almost in any pairing. There is too much historical variation.
Here is a summary of my findings below sorted by year:
always inflection, inflexion
always paralyzed, paralysed
always tire, tyre
1680 surprize, surprise
1770 surprise, surprize
1810 jewelry, jewellery
1835 colored, coloured
1835 deputize, deputise
1845 armor, armour
1845 connection, connexion
1905 aluminum, aluminium
1905 woolen, woollen
1910 esophagus, oesophagus
1910 fetus, foetus
1915 leveled, levelled
1920 center, centre
1930 savior, saviour
1940 miter, mitre
1940 specter, spectre
1970 acknowledgment, acknowledgement
1975 theater, theatre
1980 scepter, sceptre
never ameba, amoeba
never glamor, glamour
There is a lot more variation than even that summary shows; please see the more detailed charts below, including some that go the other way by showing British usage. Each of these really is a separate case, and must be considered individually. There is no single, solitary, discrete, and agreed-upon thing called American spelling versus British spelling. There is a vast continuum of conflicting tendencies, some weaving back and forth time across the Atlantic, and across time. Even when one spelling “supersedes” another, it merely comes out ahead in the popularity contest. It usually does not wholly supplant the former spelling.
For the Ngramaniacs
In all cases, the putative “American” spelling is in blue, and the putative “British” spelling is in red. Notice how the answers are all over the board, and some rather surprising, too.
center vs centre
When did center supersede centre in American English? Answer: Around 1910. Ngram
theater vs theatre
When did theater supersede theatre in American English. Answer: During the late 1970s. Ngram
armor vs armour
When did armor supersede armour in American English? Answer: Around 1850. Ngram
glamor vs glamour
When did glamor supersede glamour in American English? Answer: Never, because it has always been a minority usage. Ngram
woolen vs woollen
When did woolen supersede woollen in American English? Answer: around 1905. Ngram
tire vs tyre
When did tire supersede tyre in American English? Answer: Never, because it was always dominant. Ngram
Well, and when did tyre supersede tire in British English? Answer: in the early 1940s. But it only lasted a couple of decades before falling back into minority usage again. Ngram
miter vs mitre
When did miter supersede mitre in American English? Answer: Around 1920. Then again around 1940. Then again around 1970. Ngram
acknowledgment vs acknowledgement
When did acknowledgment supersede acknowledgement in American English? Never. It has always been that way. Ngram
What about the other way around? When did acknowledgement supersede acknowledgment in British English? Answer: Around 1970. Ngram
scepter vs sceptre
When did scepter supersede sceptre in American English? Answer: Around 1980. Ngram
savior vs saviour
When did savior supersede saviour in American English? Answer: Around 1930. Ngram
deputize vs deputise
When did deputize supersede deputise in American English? Answer: Around 1810. Ngram
But what about the other way around? When did deputise supersede deputize in British English? It’s arguable, but the general answer is that it never did. Ngram
ameba vs amoeba
When did ameba supersede amoeba in American English? Answer: Never. Ngram
jewelry vs jewellery
When did jewelry supersede jewellery in American English? Answer: Around 1810. Ngram
inflection vs inflexion
When did inflection supersede inflexion in American English? Answer: It probably never did, because it inflection was probably always the dominant spelling of that word in American publications. Ngram
The data from before 1800 is not of sufficiently high quality to use for drawing conclusions from.
But what about the other way around? When did inflexion supersede inflection in British English? Answer: Mostly never.
Or, depending on the quality of the data, perhaps around 1805. But if so, it only did so for 7 years, up through around 1812. There was a minor and short-lived blip in the early 1920s when inflexion seems to have edged out inflection again in British English for a couple years tops, and then again between 1948–1962. Since then, the inflexion spelling has been on wane in British publication such that by 2000 the inflection spelling dominated the inflexion spelling by a factor of more than 5:1. Ngram
But what about the other way around? When did connexion supersede connection in British English? Answer: Around 1820. But it only did so for around 30 years, up through around 1850. Ngram
colored vs coloured
Since this one seems to be everybody’s favorite peeve, when did colored supersede coloured in American English? Answer: Around 1840. Ngram
leveled vs levelled
When did leveled supersede levelled in American English? Answer: Around 1915. Ngram
fetus vs foetus
When did fetus supersede foetus in American English? Answer: around 1910. Ngram
Hm, but what about the other way around? When did foetus supersede fetus in British English? It didn’t: it gave up the lead around 1970. Ngram
paralyzed vs paralysed
When did paralyzed supersede paralysed in American English? Answer: Always. ngram
And the other way around: when did paralysed supersede paralyzed in British English? Answer, around 1830, but it has been losing a lot of ground recently. Ngram
specter vs spectre
When did specter supersede spectre in American English? Answer: around 1940. Ngram
esophagus vs oesophagus
When did esophagus replace oesophagus in American English? Answer: Around 1910. Ngram
But what about British usage? The answer is that oesophagus seems to have lost to esophagus around 1980, but then may have returned. It’s hard to tell. Ngram
aluminum vs aluminium
When did aluminum supersede aluminium in American English? Answer: around 1900. Ngram
And what about the other way around? When did aluminium supersede aluminum in British English? Answer: around 1850, but it has lost a great deal of ground of late. Ngram
surprize vs surprise
It turns out that surprize was once the dominant form, not surprise, but this didn’t last even a hundred years. Ngram
Then again, here is the British Ngram for the same pair. Notice that even the Brits used the z for a good while, possibly even for longer than in North America:
Summary
I hope you can now see why I said what I said: that there can be no clear answer here. Everything is different. You have to look at each word-pair separately, and you should make sure you aren’t wrong about Britain, either.
Best Answer
In the late 1700's, English spelling wasn't really well standardized. In the early 1800's, America and Great Britain standardized their spellings separately. American spellings were heavily influenced by Noah Webster's dictionary, first published in 1828. He simplified the spellings of many words, and those simplified spellings became standard American English.