Well I don't have one, so I cannot say by experience. However I do sanitize buckets and brew kettles and I can tell you I don't use 10 gallons of sanitizing solution to sanitize a 10 gallon kettle.
Personally I use starsan. If I were sanitizing that kettle I'd pour half an ounce into the bottom, turn on the water hose and spray the heck out of it till it foams up all nice with maybe 2-3 gallons of water. Then take a clean wash cloth, dip it in the solution, and wipe it all around the surface area of the interior of your conical. Keep dunking the cloth to keep it saturated with solution and make sure the entire area gets wet. Voila sanitized surface. Wipe down the lid and drain it all out through the ball valves to sanitize those.
You could even mix up say 5 gallons in there and have it deep enough to drop in all of your brew equipment for sanitizing while brewing, instead of having a bucket separate for that.
Austin Homebrew Supply
<-- 32 oz for 17 bucks, should last forever.
Or just use the iodophor you have, but make a batch in a spray bottle, just spray all surfaces with it before xfering to the fermenator. Might use 1/2 oz each time. Stuff can sit in the bottle forever, no need to remake batches.