Abuses such as this infuriate me, and I typically have a very low tolerance for them now.
Any business that is causing trouble at my expense still gets one polite attempt to contact them via their preferred means and a reasonable chance to respond, but usually only one. I'm not hanging around on the phone for more than a few minutes or waiting more than a couple of working days for a substantial response to an online message.
My next contact is normally now a recorded delivery letter sent to their registered address, which here in England is something any business with the typical legal structure must have as a matter of public record and where mail sent to it must be read. I set out my grievance, what I want them to do about it, and often at this point some compensation I want for the problem and/or subsequent trouble getting it dealt with, in a form that can become the start of a formal legal action if necessary.
This strategy has generally been enough to get whatever the problem was resolved reasonably quickly and without any further messing around. I suspect this is because anything that turns up in that form and is potentially relevant to a real legal action automatically gets passed to the business's legal team to deal with. The legal team presumably then has both the awareness to recognise a legitimate grievance and the authority to do something about it rather than let it escalate.
I don't like that this seems to have become necessary to get a reasonable response from a lot of large businesses today, but fortunately for all of us in my country, there isn't actually any obligation to play by the business's rules in a dispute if they're giving us the run-around.