Blah, blah, blah, there have been problems with the invite system for months, and they keep towing the line it's us, not them.
On the email account front. I never send an invite to anyone who gives me their work email address. I'm saving them from themselves. It might get caught in the corp spammer, and it shouldn't be sent to their work address to begin with. I have multiple email accounts, biz, family, shop, gene, etc., like most sane people.