It looks like this is just a bug in Xcode7. The documentation says that the "Reset" button means the certificate is invalid and needs to be regenerated. The certificates are fine because I created and used them very recently. However, I created them recently because the old ones had expired. So, I went ahead and clicked the reset button for the ones I wasn't using. That seems to have fixed them. They were revoked and re-generated. Now Xcode7 is happy with them. Plus, Xcode7 can now export them so that I can use them on Xcode6.
The moral of the story? If you want to do anything with Apple beta software, you need a full "burner" ecosystem. Machines, devices, Apple IDs, even paid Developer accounts. Otherwise, your apps are hosed for good. Case in point. I learned this lesson last year with Xcode6. It created duplicate developer IDs which can't be revoked. Now, Xcode7 also wants to reset my developer IDs. But does it want to reset the ones I was using or the duplicates that Xcode6 created? No way to tell. No worries now because this old account is now my "burner" account. I won't have to sell any apps from it in the future so I don't even have to worry about yet another futile attempt to change my address with Apple.