I'm not sure there's anything I really could have done. I was working on 30 day terms (quite common), and I'd worked for them with quite prompt payment for over a year. I probably had ~12-15 paid invoices from them for similar amounts that were paid within 7-14 days of issue.
I stopped working for them upon the issuance of the second invoice in question - so I had two invoices outstanding at that point, 1 that was 15 days past issue (but not contractually due) and 1 just issued.
Do people in multi-invoice contracts really stop work until they have proof of remittance? I've never heard of such a thing - that sounds crazy to me.
I know you edited your post saying you would't, but do NOT do anything to their codebase/website etc. Don't even remotely entertain the idea.
Similarly, don't spout anything libellous incase they end up going on the offensive.
Best thing you could do is pick up the phone and actually call them and give them a chance to respond (they're humans just like you) and if they dodge your calls, go for a debt collection service.
My experience was that the highest value clients paid somewhere in the net 45 to 90 range, despite contracts stating that we billed net 30 that included penalties and interest. And my experience was that it was actually fairly easy to increase prices by 25%, but extraordinarily difficult to get clients to agree to unusual terms (such as a halt in the performance of the contract in the case of minor payment delinquency).
I'm not saying my experience is the only experience, but frankly the only clients who I could imagine agreeing to those terms were puny, and unsophisticated folks who you probably don't want to work for anyway. The more sophisticated buyers all had a lawyer who would negotiate anything like that out of the contract anyway.
https://en.wikipedia.org/wiki/Blind_men_and_an_elephant
Yes, I have consulted for everything from startups to large multinationals but your experience may be more common/normal/relevant for HN readers. With the most recent multinational client, it took some time for my contracts to go through legal but they approved everything without any changes.
So if their LLC(Whatever) fails, they're still on the hook.
Banks do this for every loan my small business has taken. You sign for your company, but you also sign personally. If they won't do this, move on.
Lesson learned.
EDIT: I think people aren't giving you enough credit here. Every contract is a negotiation - this clause is just another weapon I can include in my starting offer on a new contract. If people say hey, we won't agree to this provision, I can now say "OK, no problem, my rates just went up 10%."