I just did a definitive test on the times to boil 6 gallons of water on my gas stovetop. This is a plain jane gas burner stovetop in a rented apt.; estimated BTU per burner is 5k BTU.
From front to back, my burners are 12" apart measuring from the outer edge of each burner. I put my 10 gallon pot which is 13.6 inches in diameter across both as evenly as I could, filled it with 6 gallons of tap water, placed foil around the edges of the lid to get the best possible seal, then cranked the gas on both burners, and checked the temp of the water at 15 minutes intervals.
Time Temp
0 minutes 80 deg F
15 minutes 120 deg F
30 minutes 155 deg F
45 minutes 182 deg F
60 minutes 205 deg F -piddly boil
75 minutes 212 deg F -rolling boil
So what does all this mean?
1) Yes, you can get a full boil on the stovetop with 6 gallons of water.
2) Probably, a wider pot would catch more heat and boil faster. About 1/3 and maybe even 1/2 of the flames from both burners were actually riding up outside of the pot and not underneath.
3) I will be upgrading to a kettle that is 15.25 inches diameter. And that will catch more heat from the burners underneath the pot, boil faster, and allow for ridiculously big 5 gallon batches without spillage.
Boom. Upgrade time.