With regard to using a random public mint, personally, I wouldn't even bother with multiple mints. The "small amounts" rule is sufficient mitigation in my book.

I recently learned that mints will effectively invalidate tokens that have been dormant for a while, by design, in order to clear out tokens that are presumed abandoned and keep their database of outstanding tokens manageable (or maybe other reasons as well? 🤷‍♂️) What constitutes "dormant for a while" may be years, or it may be weeks, or it may be whatever. Presumedly, that policy is up to each individual mint.

For this reason, I think trying to manage "small amounts" of tokens across multiple mints is bound to be more trouble than it's worth.