My first idea is to email Blogger support to ask if anyone has a GMail invite to share. Hey, it's worth a try!
I had a related thought today. I decided to email a GMail account (guessing that it had been registered) of the name of the city I live in. I then politely requestd a GMail invite to a fellow city-dweller. I don't really hold out a lot of hope for this attempt but again, it was worth a try.
I've also entered a few blog contests - we'll see what happens with those.
I have posted my swapping idea on http://www.gmailswap.com
I visited the IRC room #orkut thinking there might be some people there with GMail invitations to share. I did get an Orkut invite (thank you Ian) but sadly no GMail invite.
I've logged into the IRC room #gmail but nobody was talking.