“..it cannot connect to any wireless network, so we don’t have to worry about it doing so maliciously. We’ve also taken other measures to frustrate attackers, for example we have physically removed the hard drive so there is no way to persist data on the laptop itself”

Hopefully by physically removing where possible? Also consider microphone and speakers if you’ve not already..

Can a white noise machine help there? https://ggerganov.github.io/jekyll/update/2018/11/30/keytap-... says the method is sensitive to noise.

Airgapped machines ought to be housed in an airgapped room, equivalent to a SCIF.

You could let the system ask the characters of the passwords in random order. It would be a bit of a hassle, but gives some added protection for largish passwords.