Coincidentally. And maybe a solution.
I've been re-reading Gene Kranz' book "Failure Is Not An Option". Last night I read the section on Apollo 11 and Neil's exit.
He quotes Neil as saying "- - - small step for man, - - - " and, indeed, that's what he said.
However, the literary device of correcting or clarifying quotes seems appropriate. Just put the "a" in parentheses.
"That's one small step for (a) man, one giant leap for mankind.'
For me that would satisfy everything. An accurate quote in every respect. I'm sure someone has thought of this already, but I haven't seen it.
Arf