The good news is that I can inquire about such things by using Kaiser's online message center. And they commit to get back to you within 48 hours.
The bad news is that I submitted my question last Monday and hadn't heard back at all.
The stupid news is that I discovered, when I went back online to my Member Center to fin a phone number to call, that they don't auto-email you when any of your submitted questions receive a response. No, you have to go back and check your message center proactively.
The good news is: When I actually looked my doctor's office had responded the very day I submitted the question!
The bad news is: I let a week go by waiting for an email to show up.
And while I was stewing about the lack of responsiveness, it wasn't Kaiser; it was me.
Hate it when I'm wrong :)
Anyway, called Kaiser Travel Clinic to find out what's what, and they'll be calling me back in the morning. Nobody likes shots, and it looks like I'll have to get a bunch. Hope it's worth being a human pincushion for!