I have the K3 wifi and it only usually takes less than a minute for me to receive what I've sent on my K3. (the one exception was Saturday when they updated everyone's software)
The big difference between sending it to
name@Kindle.com and to
name@free.Kindle.com is that I get a supplimental email from Amazon saying my document is on it's way when I use free.kindle.com. Everything I send is from within Calibre, which is why it doesn't sound like a Calibre issue to me. If you'd like to personal mail me and include a print screen of your mail preferences screen, I'll see if I see any anomalies.
cheers