If you are able to reach a boil in 6 gallons with 2000W, which I am hesitant to say that you can (no insulation?) Here is the breakdown.
Not including heat loss, after you reach a boil:
970 BTUs required to boil off 1 POUND of water.
2kW is 6,800 BTUs
6,800 BTUs /970 BTUs = 7 pounds
So you will boil off less than a gallon in 1 hour with 2kw.
The problem is that your numbers posted from heating in a cooler show that you are less than 50% eff with the bucket heater trying to heat in the cooler. So it is possible that you will boil off less than .5 gal even with 2kW in the boil kettle due to heat losses.
From 160F to a boil in 6 gallons will require 2500 BTUs, according to your previous numbers posted, this will take 45 min. to accomplish. It will be a simmer when you do get there, and you will boil off .4 gallons in 60 minutes, according to your test #s, no worries about being too vigorous.
To boil off 1.5 gallons in an hour requires 12,100 BTUs of energy. If you are boiling for 60 minutes, this is a MINIMUM of 4kW, or 4000W of energy, for example