As reported on Wikipedia (Rhotic and non-rhotic accents), English had become non-rhotic by the end of the 18th century; John Walker used the spelling ar for the pronunciation of aunt in 1775, and reported caad as pronunciation of card in 1791.
British colonization of the Americas began in 1607 in Virginia, even though there had been previous attempts in 1586 and 1587. United States of America declared its independence on July 4 1776, when the non-rhotic accent had started to spread on Southern England.
Mostly they're not recorded.
They're called Hesitation Markers, or various equivalent names. They are the various sounds people make when they're hesitating to think of what to say next, or to remember a word, or just because they've drawn a blank. Emitting one of these markers signals an intention to hold the floor, and to try to keep one's conversation partners from taking the floor and interrupting one. These markers vary, from group to group, and language to language.
They're phenomena of Speech, though, not of writing. So, unless you're transcribing dialog, you shouldn't have to worry about how they're spelled. Which is good, because they're spelled any which way at all.
However, any spelling with an "R" in it comes from a non-rhotic dialect of English, like RP in the UK. And "UH" is a lame attempt to represent shwa - /ə/ - the commonest vowel in English, and the commonest hesitation marker. E.g,
- He said .. /ə/ .. he said he wasn't .. /ə/ .. going to arrive on time.
How you spell it is up to you. The Academy hasn't ruled on that yet.
Best Answer
In addition to rhymes and dictionaries already noted, you can cite spelling shifts in which the "r" letter positioned after a vowel disappears from certain words.
The Wikipedia article about Rhotic and non-rhotic accents cites
which is more or less the time frame in the question. This shows, assuming the spelling evolution follows the pronunciation shift, that in this words the rhotic pronunciation had disappeared as well.
Also have a look to a contemporary phenomenon named "The Great vowel shift".