It turns out that although you can't directly sign up for Writely during this transition to Google, existing Writely accounts can invite others to Writely to collaborate on existing documents. Once in, a new collaborator has a full-fledged Writely account.
A generous donor just gave me the Writely invite I have coveted for these months. Woo hoo! Actually, I find Writely quite comparable to ZohoWriter, another free online word processor which freely allows new registration. ZohoWriter is excellent.
But so is Writely, and I assume you're here for one of the Writely invites I can now give away. Post a comment to this post and I'll send you a Writely invite. After you get the invite and click on it, you will choose a password for yourself. If after that you get an error saying you can't view the document, don't worry. Just go to the Writely home page and you'll see that you have a Writely account.
I imagine I'll tire of checking the comments of this blog eventually, so at some point I'll close off comments to this post. Please don't email me directly for these.
Update: I'm closing comments, as Writely has just opened up free registrations.