Based on that, I propose we push for ‘it’ as a sole singular pronoun (and keep ‘they’ for plural, as knowing if someone is referring to one or many is far more useful in almost all contexts than knowing whether they are referring to a man or a woman (or ship, or country, etc.), and those few contexts where it is relevant should be easy enough to glean from other information.
If you think that could never work, I'd point out that Mandarin managed without gender-specific pronouns until contact with Europeans, and even now they are only distinguishable in written form.[1]
Alternatively, there's Stallman's proposal for ‘person’, ‘per’ and ‘pers’.[2] I'm doubtful of any proposal that involves creating new words (see ‘xe’, Spivak pronouns, etc. ), but everything else Stallman says seems to come to pass so maybe.
[0] https://en.wikipedia.org/wiki/Gender_in_English#Decline_of_g...