"making them wait was jeopardizing the very existence of their business"
Had a similar line from a client. I had done the work and the invoice for £lots was seriously overdue.
I had sent reminders and all invoices and statements included (in bold) "We understand and will exercise our statutory right to claim interest and compensation for debt recovery costs under the late payment legislation if we are not paid according to agreed credit terms".
The last time I called them I was told "If we pay you we won't be able to pay our staff" - to which I replied "if you don't pay me, I can't pay me".
They obviously thought, as I was a one-man-band, that they could get away with it.
I contacted a debt collection agency, who, for a fee of £2.50, sent a "letter before action". I have no idea what it said, but funds to cover the invoice, statutory interest and £2.50 fee arrived as soon as it was received.
I later learned that another business that I worked with had the same problem with this lot, so I pointed them to my friendly debt collectors...