Supposed you are only interested in VIP providers who require that you have be verified, PLUS 1 or 2 referrences. How likely is it to get an exception, or would I be just wasting my/her time?

No way to tell without asking. If you don't have any refs, it might be real tough.  I would suggest seeing some newbie-friendly providers so you can have some references.  The alternative is to join one of the verification sites, like DateCheck, Preferred411, or RoomService200.  Until you have refs, you prob can't be so picky on who you see.

Good luck.

I noticed in your post you referred to "VIP providers"  In the future don't pay any attention to the VIP. it's just a marketing ploy. Kind of like new and improved.   A provider is a provider, regardless if it says VIP, it means zip.

I give references but no personal info aside from my P411 and Date-Check IDs. Yet I often get approved by providers whose website may say that they also require my full name, work info, etc. For them, apparently, a verification site serves the same purpose.

I expect that their need for at least one reference would be harder to set aside. You could ask, however they might not appreciate it when their policy is already so clearly stated.