Second Burner mission was offered earlier today. I once again pulled the Sansha flavor, which makes setup very simple.
As the server seems at least a little bit unstable (not sure if it was my connection or the game), I'll wait until it's not super-busy-Sunday before I tackle it.
Total mission count between #1 and #2 was somewhere around 25-30, including declined missions. I'll keep a better count this time.
I did notice that they promised payout this time includes just short of 14.2k LP, which isn't too shabby. Base payout is 1.67M with a time bonus of 2.18M isk, which still feels too low.
I intend to follow the same basic recipe as attempt #1, which resulted in success.