... the ids are meant to be relatively human readable ...

If the ids might be spoken (say, to an agent over the phone), you might consider producing them according to an easy-to-speak, easy-to-hear pattern. Something like

Consonant-vowel-consonant-digit
Consonant-vowel-consonant-digit

By using a predictable pattern, miscommunication is minimized. Since an agent knows to listen for a digit in the fourth and eighth position, zero and one are unambiguous.

If you're concerned about accidentally generating "dirty" words, try

Consonant-consonant-vowel-digit
Consonant-consonant-vowel-digit

This lessens the odds.