I've been with a few agencies for many years so please take this advice with a grain of salt.  

I've been successful getting verified with new agencies that pop up.  I don't use my old agencies as references for new ones - not sure why, but I just don't.  

I fill out the online form, I keep it vague, I don't answer everything, and I see what they come back to me with.  Remember, it's not a job application.  If they don't answer in a day, I text.  Maybe I fill out the form a second time and text. No luck? I move on.  Plenty of fish in the sea.

They seem to have different levels of verification - some want a picture of your drivers license (no thanks).  One asked for a selfie with today's paper (weird and... nope... who has newspapers anyway?).  One was okay with a linked-in link and a selfie.  I thought for a while about about this but figured linked-in is already on the internet and I've got selfies posted on social media so....  

There's enough agencies out there that I'd say just start chipping away at them and I bet eventually come across one that's at your comfort level and will take you.  Be patient, try not to get frustrated, and you'll likely be rewarded.      

Ha.  "come across one"  I didn't even try to do that.

When you eventually do become a client just follow the golden rule: Be cool.  
If they screw up booking... be cool about it.  
If a provider doesn't look or perform like you wanted, maybe she's just having a bad day... be cool about it.  

You can state your case on here the next day.  

Nobody bats 1000.  Show 'em a little grace in the moment and they'll eventually recognize you as a good client... and that's a good thing.