Jeff: Yes, each line has it's own progressive. There is a special bonus for hitting a Royal on all 3 lines at once, but how it is calculated exactly I am not sure. The $5,800+ was not the total of all 3 progressives. Those were $1,200+ on Line 1, $1,100+ on Line 2, $1,000+ on Line 3, so those 3 line totals did not equal the $5,800+. Maybe someone else can answer.
One of my most favorite hands dealt on the Bonus Poker progressive last night was bonus four 2's on 3 lines--dealt to me.
Also, after the RF, I must have had 4 to a Royal dealt 4 different times. 4 to a Royal on all 3 lines! That's 3 times the exasperation when the 5th one does not appear.