In reply to The Armchair Mountaineer: I think you have answered you own question. You heel strike hard.
It seems that you need to work on your running technique, you obviously have the fitness, but that may be your problem i.e. too much too soon.
If you do some short runs focusing 100% on your technique rather than setting distance/time goals.
Listen to your body.
I could suggest you try non padded shoes, to highlight your problems much quicker, so that you may alter your style accordingly. The padding in shoes hides faults in technique. Like wearing a thick pair of gloves when typing.
I'm sure the anti minimalist shoe brigade will be along shortly, decrying everything I've said though.
If it's causing permanent pain a visit to the doc is probably advisable first though.