Empirical bound on sum of electron and proton charge

Followup to "Why do electron and proton have the same but opposite electric charge?".

It is argued that even a tiny residual charge would result in huge amounts of electricity in bulk matter, everything would be different, etc. I do not find that a convincing answer: suppose $n$ protons plus $n+1$ electrons are neutral. Why wouldn't we also expect there to be $n$ protons to every $n+1$ electrons? That is, there is no bulk matter problem if every $n$'th atom is a negative ion (for hydrogen).

Now, what empirical lower bound can we give for $n$ in that kind of scenario?