Well, I just tried a random date in March (10th), and there are no K's available. That leaves you with either:
S (base) roundtrip for £1,025 + tax. (Premium Economy flexible - companionable)
L (base) roundtrip for £725 + tax. (Economy upgradeable)
Children 2 through 11 are only charged 67%, so that makes them £687 and £486 respectively.
So... technically, you could use miles to get a companion ticket against your own S class for the missus & upgrade two L (economy) tickets to Premium using miles as well. Having never upgraded a kid's ticket with miles, I'm not 100% certain of the possibility, but I assume it can be done (?)
Meaning:
* You in Upper (£1,025 + tax + 40k miles return)
* Missus in Premium as a companion (either a companion ticket - c. card? or 30k miles
* 2 kids in Premium (£972 total + tax, + 20k miles each return (40k total))
Total cash = £1,997 + taxes
Total miles = 80k/110k (depending on whether you have a c. card companion ticket)
Obvious problem being that you either need a credit card companion ticket, or additional miles to achieve this. If you have/can get them, I think this would be the cheapest way for 1 x J & 3 x W.