The phrases "good people", "good souls", "good citizens", "good soldiers" and "good Americans" all would have been better than "good men", depending on your focus. I think "good souls" would have been the most poetic of these phrases for your intent.
If you mean to include the members of the Merchant Marine or the CIA who have died to support US military policies, then "soldiers" doesn't work.
If you mean to include the members of the Peace Corp who have died to support US non-military policies, then "soldiers" also doesn't work.
If you mean to include the American solders who are not US citizens, then neither "citizen" nor "American" would work.
If you mean to include the many female soldiers who have died in American conflicts, then "good men" doesn't work. While "man" can include all people (reflecting its Germanic roots), a phrase like "The show is especially popular with middle-aged men" is almost universally understood to be different than "The show is especially popular with middle-aged people", nor does the door marked "Men" indicate the gender neutral bathroom. We are also not long from the time when women were excluded from organizations on the justification the bylaws specify men, or from the time when "research men" and "typist girls" worked together as "he" and "she" respectively.
As to your Armstrong quote, your term "fix" confuses me. The past simply is. We can change our understanding of the past, and understand it's context in different ways. We can change how we do things in the future. But we cannot "fix" the past.
Still, I will consider an alternative history where the first moon landing were to occur this summer, with a male pilot named Armstrong2. You already saw that I am not against using the gendered term "wife" (derived, by the way, from 'wif', meaning a female man. When "man" was a gender neutral term, she would have been a wifman and I a werman, meaning a male man). I see no reason for Armstrong2 say 'small step for a man or a womyn' when "man" is a better fit and non-exclusionary. (If Armstrong2 were a woman, would you not think 'that's one small step for a woman, one giant leap for mankind' to be somewhat odd?)
You brought up 'womyn'. I believe you did it as a debate technique to polarize to topic and make a false association by assuming that a small group of feminists is representative of the whole of "SJW". Still, I will consider that possibility.
If Armstrong2 were to say "one giant leap for man- and womyn-kind" then that would be an expression of Armstrong2's views of gender identity. Is that what you think Armstrong2 believes? If so, then what's wrong with that statement?
I can answer that. The Armstrong in our timeline wanted an inclusive term. 1969 was the time of upheaval in race relations, gender relations, and international relations. He wanted a term that could encompass everyone, and do so in a poetic, memorable statement. If Armstrong2 were to say 'man- and womyn-kind' in the alternative timeline similar to our modern one, it would be a divisive phrase. If "man-kind" really meant everyone then there's no need to say "womyn-kind". If "man-kind" is limited to just males, then those woman who do not accept the aspirational goals behind "womyn" would feel excluded. This would be most of the women on the planet. Therefore, "man- and womyn-kind" would not be an encompassing phrase.
Hence why I think your objection has no merit, and your proposed phrase fails to capture the intent behind Armstrong's quote. I can of course think of many alternatives, but don't see the point. Nothing I write can shine against the excitement and glory that imbues that first trip to the moon. I can, however, say that "That's one small step for a man, one giant leap for humanity" is a better alternative than what you proposed.
Tell me, do you still use the terms "aviatrix" and "authoress", "poetess" and "doctress", or have you embraced that butchering of the English language? Or do you somehow believe the terms you grew up with are the correct ones, and not the result of the generations of butchering the language that came before you?