How do I transfer my all of my cloud services, databases, virtual machines and blob storage to another subscription that I newly subscribed to? Is there a simpler way?
I have just contact Azure Support about this. Their answer:
[Azure Support] will be able to migrate the Windows Azure data (hosted services, storage accounts), VM instances, service bus, Web Sites from source to destination subscription... Please note that the Preview feature services are not supported for migration, however we can do it on a trial an error basis.
So it seems this can be done via support now. The big caveat is that it's (currently, at least) an all-or-nothing move. So you can't move everything except for one service, or one storage account, etc. You have to move everything.
Note that moving a SQL Azure server is trivially done through the management portal.
Update: I have completed a subscription transfer as mentioned above. The actual transfer was a fairly painless process that only took a few hours. Getting all the various services split out into separate subscriptions was quite painful. So the moral of the story is to be careful about what services you put into a subscription. If at all possible put each "product" (website, SaaS offering, whatever) into a separate subscription.