Esperanto Beta only took me less than 35 days, so this sentence could be very accurate for a lot of people!
I'm curious why the -e ending is used here. Is ĉi-monato not correct? Can ĉi only be used with adverbs and correlatives? Or does it imply that we're doing it this month, and will continue to do it into the future?
Yes, ĉi-monato is wrong.
"Ĉi monato", without the hyphen, could be shorthand for "ĉi tiu monato" which means "this month", but it's a noun phrase, not an adverbial.
So the sentence would be ungrammatical because it would seem to have two subjects.
Using ĉi as a separate word, without a word from the ti- group, is a bit unusual and I would recommend avoiding it.
So, stick with ĉi + ti-, or ĉi- (with hyphen) + adverbs.