Hi Bryan,
Thank you for your compliment and for you intelligent question. In answer to your question, the reason that European banks holding the debt of other member states amplifies the crisis is this...
If the governments fail, as it looked like they might in 2011, then that would collapse the capital of the banks since they owned so much sovereign debt. In turn, the banks were backed by the very sovereigns that might have failed. This creates a vicious circle that works in both directions. So if the banks failed due to poorly underwritten loans and poor returns on proprietary investments then their capital would collapse, necessitating a bailout by governments that are also highly levered. Bailouts would threaten sovereign solvency which then would further damage bank balance sheets. Ouch!
Hope that helps!
Jason