Has the problem gone away with the new battery? Maybe the swollen battery indicated a higher then normal temperature in the battery, and it's that higher temperature in the battery that caused the phone to shut down and restart every 30-45 seconds.
When you received your second GS2, did you get a new battery or did you use your old one? Are you on Gingerbread or ICS?
I think we've exhausted all the possibilities. It has to be either hardware, software, or pilot error!