Without knowing the details about your services and infrastructure, it's hard for me to know what's involved in going multi-region now. Are you sure it's such a a gargantuan effort? I would've thought one person working full-time on this for a week or two would be enough, but again I don't know the details of your setup.
One option would be to pay a consultant who is an expert in Azure/cloud stuff to come in and help. May not be cheap, but could be a lot better and quicker for you and better for the business, especially if none of you are really big experts in Azure.
I've been here before (I think)...had to wear many hats and scramble to make sales, build the tech, act as de facto DevOps person even without a lot of experience doing it, etc. That is the way, but stuff happens.
Happy to chat about specifics if you want to bounce ideas off of me or go through your particular situation. Can't promise I'll have concrete advice, but happy to talk it through.
Very poor position to be in, apparently this happened in azure UK recently too.
Let the scar you get from this is be a learning experience, hopefully you will not fall into the same trap again to trust this company.
In my career I'm in a place where anyone suggesting I do work on Azure gets an instant doubling of my asking day-rate and I really hope the will be put off and find another victim for this gig.
That said, another learning experience would be to use terraform or something (tbh for azure the only sane thing is terraform, ARM templates are just garbage). Having terraformed your one region switching to the other would be much easier, tho not trivial.