My own bet is that Heatons produced their own dies in 1882, just as they almost certainly did in 1874 and 1876.
1874 was a mixed London mint/Heaton mint year, yet reverse I was clearly unique to Heatons. Plus they were the first to use obverse 8 (Freemans 77 & 78), an obverse not used by the London mint in 1874. So did they produce this and London were sufficiently impressed with it to adopt it themselves from 1875 to 1879.
Reverse K was also used solely by Heatons in 1876, and then only fleetingly by the London Mint in 1879.
As you say though we'll never know for sure.