This opens up the whole subject of what exactly did Heatons do - did they produce punches for whole dies from master matrices issued by London? Or did they get sent dies that just needed the final digit and mintmark punched in?
Given that the reverse dies for 1882 are different between London and Birmingham, that implies the former. However, it could equally be that Heatons were sent quantities of a particular reverse design, and that the London reverse was produced separately solely for the purposes of testing the electronic presses. Since Heatons needed to produce pennies dated both 1881 and 1882, it's entirely possible that they decided to repunch a single 1881H die, especially given the large quantities of 1882 required. They would never have been sent the London reverse (which perhaps was done after the bulk of the issue had already been done by Heatons?) which of course makes identifying a genuine London 1882 easier.
Over to the predecimal hive mind...