I had let it slip, and let it slip, and finally this evening burned my why thru a pile of paperwork until it came up. I filled out the form, and then when to the WA DOL's website to find my closest "licensing agent" and find out what the fee was going to be.
Turns out that I can fill out and submit the same form online. For free. So I did.
It like the DOL has gone web enabled in a big way. The whole "independent licencing agency" scam, and also the whole traditional "stand in line at the DMV" scene is fading like a bad dream.
What *really* amazed me was that it worked Just Fine in Mozilla on Linux, and refrained from any IEisms and from any fancy JavaShit.