With a 100% efficient, ideal system, it would have taken a .9kW unit 40 minutes to move 3 gallons of water 61 deg C.

That means your setup is 70% efficient, which seems low considering the apparent 92+% efficiency of that Luxine system. more on that later...

So, I would estimate that it would take your unit (at an actual output of 910W) around 30 minutes to move 6 gallons of water 24 deg C (from 76 C to 100 C).

A 2500W unit at 80% efficiency should take 3 gallons of water from ~68 F to boiling in a little under 25 minutes. I estimate that your 1300W setup would accomplish the same feat in 50 minutes.

In terms of energy :

move 3 gal 61 deg C - 692,350 calories OR 2745 BTU

move 6 gal 24 deg C - 544,800 calories OR 2160 BTU

move 3 gal 78 deg C - 885,400 calories OR 3510 BTU

(food calories are actually kilocalories)

The More-On-That-Later-Section :

Did you have a lid on?

Do you know if your unit is one of the kind that will go maximum power for a while and then cool the inductor coil down?

Was it breezy/cold in the heating area?

Did you use an insulated heating vessel?

Of course, maybe that's just standard efficiency, Luxine has a chart that says a generic 2.6kW unit is only about 80% efficient, and more power seems to translate to more effienct, especially if you use a Luxine. *shrug* It'd be interesting to find out the efficiencies of other units.

http://www.luxine.com/advantage.php
Keep in mind that my calculations are pretty simple and they don't take into account fun things like evaporation (lid), loss of heat to the air (except in the "efficiency" sense), etc.

Sorry the reply took so long, Thanksgiving vacation means no math!