The opinions do vary dramatically, you're right. It's a tough formula to put on paper, because so much of what people will quote you comes from the aquarium world - like 10 gallons for every inch of fish. The problem is 14 one-inch goldfish are no where near the biomass of one 14 inch koi. I'd put 28 goldfish in a 500 gallon pond, but I wouldn't put 2 14 inch koi in the same pond. Mainly because at 14 inches, a koi may be only half grown. So sure, you could put a dozen tiny koi in your pond and be fine... for a while. The problems start 5 or 6 years down the road. That's when people show up here and say "I don't understand... everything has been FINE up until now..."
In my personal, non-scientific opinion the 1000 gallon minimum for the first koi is a good start and a couple hundred gallons for each additional koi after that. Calculate what that comes out to and then plan for less. No one benefits from overcrowding. The problem though is we all know we SHOULDN'T get another fish and we do it anyway!
And yes, filtration plays a big role, but the best filtration in the world will not be enough at some point. And how much work do you want to put into maintaining your filtration? A well balanced pond requires very little work on your part. A koi pond with heavy duty filtration is much more labor intensive.
By the way, if your measurements are right, your pond is more like 2400 gallons (I used a 3 foot average depth).