For an alternative, maybe relay the texts to a slack channel (that's easy enough to receive on a phone for your coworkers). Zapier can probably integrate twilio/slack quickly.
Yes, I will do something like this. However it doesn't alleviate the overarching concern that they are behaving in a way that treats my business very recklessly.
I use Slack like this for various notifications. I just setup a new Slack instance and created channels for each notification area (smart home, media server, etc). Now all the software in those various areas can send messages (via webhook) and I can set the alert preferences per channel. Makes it easy to quickly look at Slack and know things are running fine.
I also have a #critical channel anything can post to that always has alerts enabled on my phone so I don't miss anything important.