ERB says I'm projected for assignment to W3VZAA, but my 1SG says there are no slots there for my rank. What else could that mean?

PCS'ing can be a trying time. I wouldn't read into it too much if they have slots or not, if they Army is telling you that you are leaving, then you are leaving. As others have pointed out, you are probably filling a slot right after someone else leaves, so seeing if that slot is available today is meaningless. Just make sure to make your appointments, if your married and want to live on post make sure to put in for housing ASAP, and have a positive attitude. The Army is all about new beginnings, just keep an open mind.

When are you slotted to PCS? There may be someone there that is in the process of being slotted for a PCS of their own.

You're S1 won't find slots because they're looking at open requisitions. You're on a filled requisition and if they wanted they can look at your requisition number to see that's where you are assigned.
AMEDD C&S is a big places and covers several battalions. Your assignment will always project you to a higher level (usually brigade level) and when you arrive you receive orders to the subordinate command you'll be assigned to.