Those examples work the same way as when using pronouns for several people with the same gendered pronouns. For example:
Traditional grammar: He hated the food, but he liked it.
Probable fix: Maximiliano hated the food, but Abooksigun liked it.
The trick seems to be, as usual, being mindful of when one has established what pronoun is being used for whom, and when it risks being mistaken for anyone else. I have an in-law who is terrible at this even with gendered pronouns, and even after years they are still surprised if you don’t know who is being referred to. “I spoke with your mom today, and he said that he’ll call back later.”
But also, “traditional” really is a loaded term. Because it tends to be used to lend a practice broad legitimacy when no traditions are universal. It might not be prudent to assume that your traditions are those of others with whom you speak. They might be, but it never hurts to ask.