Probably similar to First Person Models issue: tr7zw/FirstPersonModel#227

They solved it recently by injecting before FAPI, since their ArmorRenderer likes to override anything else.
tr7zw/FirstPersonModel@54608f8

I was told about this issue via discord earlier today, so I've actually already fixed it in the latest commit using a similar method to what you mention and a mixin into FAPI. If you'd made this issue two hours earlier it might've saved me a bit of searching 😅. no worries though.

I'll backport these changes to 1.18.2, and push a release after that. Expect to see it within the hour.