After reading up on a few boards about K-girls, I'm thinking about trying out the experience, but all the talk about the screening process is pretty intimidating.

I've been around and have posted some reviews, and I am verified using P411 and DC, but I get the impression that none of this will really help.

What is the local screening process like?  How long does it take?

It's not intimidating, but you just shouldn't have any expectations. If they can't take any new clients they won't reply, and you shouldn't take it personally.  

Recently I contacted an agency where I had previously seen 4 girls with no problems and had no reply.

Then I contacted a new agency and was cleared in about an hour.

My suggestion would be to try one that has recent/active ads here or on other sites (means they are looking for new clients), and email the info they want the day before you would like to have a session. If they don't reply, try another one

You've seen Mischa in Seattle, a K-girl legend, and gave her a 7/5. K-girls may not be your cup of tea.