In this sentence:
The teller would refuse (a/an) 1149 penny payment.
"1149" could be pronounced "one thousand one hundred forty nine", or it could be pronounced "eleven hundred forty nine". One way would take "a"; the other would take "an". Assuming I don't want to spell out the number or rephrase the sentence, which article should I use?
You always use the one that corresponds to your pronunciation. Spelling doesn't matter.
Writing represents speech, not vice versa. You write it like you say it, however that may be.
It’s the same thing when writing something like “an herb” versus “a herb”: you write whichever one you actually say, depending on whether you pronounce the leading h-.
I would sidestep that problem by writing, "The teller would refuse a payment of 1149 pennies."
Also note in your original version you would need a hyphen in "1149-penny payment".
