Are you one of these people?
https://www.dictionary.com/browse/fortuitous
> Many object to the use of fortuitous to mean simply “fortunate” and insist that it should be limited to its original sense of “accidental.” In modern standard use, however, fortuitous almost always carries the senses both of accident or chance and luck or fortune. It is infrequently used in its sense of “accidental” without the suggestion of good luck, and even less frequently in the sense “lucky” without at least a suggestion of accident or chance
In any case, neither of these words is the right choice in the context of the previous comment. A word like "incredible" or "unlikely" or "amazing" would more clearly express the idea.
I disagree. Fortuitous/fortunate/lucky/convenient all work better.
Compare the usage of "luckily" in this quote from The Naked Gun 2½: The Smell of Fear:
https://www.imdb.com/title/tt0102510/quotes/?item=qt0434008
> Commissioner Anabell Brumford: Ladies and gentlemen, I would now like to introduce a most special American. Tonight, he is being honoured for his 1000th drug-dealer killed.
> Lt. Frank Drebin: [to applause] Thank you. But, in all honesty, the last three I backed over with my car. Luckily, they turned out to be drug-dealers.
Here, "luckily" gives the dark implication that the police covered up Drebin's killing of three people by posthumously framing them as drug-dealers... and maybe the other 997 people as well. "Luckily" is nicely understated where "amazingly" would be too obvious, and "incredibly" doesn't work at all.
But "so fortuitous a coinicidence" is redundant and confusing; it means, basically, "so coincidental a coincidence".