I've just returned from a nice vacation, so expect things to heat up again here soon!
An interesting thing happened while I was gone - the site went down HARD. The reason it went down is likely due to some intricacies in how Orchard works in Azure. Long story short, my deployment didn't contain assemblies for a number of assemblies that orchard likes to have since they aren't marked private or copy local in the solution and they were present in my GAC. I had manually copied them over, which I now know is a big no-no, because when the instance was rebooted (I think to apply some updates), those assemblies were wiped. Users accessing the site then got the YSOD. I attempted to correct the problem by re-copying them over (RDP'ed into an RDP from a borrowed MacBook Air and 6k miles from my desktop), but I think I may have flipped Orchard over into Safe Mode by doing so. After returning home last night, I've carefully re-deployed Orchard with a fixed Orchard.Azure.Web project file, and everything seems to be working now. Phew! There's not many things more agonizing than knowing your public presence is down and not being able to do much about it!
Maybe since the site is so new that nobody really noticed? <g>