We old codgers still use the politically incorrect generic "he" as well, knowing, as we didnin the 1970s, 1960s, and centuries earlier, that it was not gender-specific when used in such context. Never acquiesce to those who care about impression more than context.

For those who do want to use a gender-neutral singular, it is absolutely acceptable to do so as long as it is grammatically accurate (i.e., does not open the door to ambiguity of meaning). Your reference to "human", etc., are good choices. Another option (albeit, not universally accepted) is to use the archaic generic classifications: "ge", "gen", "ger" (subject, object, possesive).

In general, one should not use "it" for human beings.