Does anyone know what's actually required for the Lion of the North achievement?

I'm playing Sweden for my first ironman run, and it's going really well. I just hit the late 1500s and the Wars of Religion situation just popped, and I realized I have a problem. Apparently, you HAVE to be in the HRE to join either side of the League? And unfortunately, I flipped to Lutheran nearly a century ago, so I'm ineligible to join.

Am I just locked out of the achievement now? Are you expected to join the HRE as Sweden?? That wouldn't make any sense.