It has struck me that a character can suffer further damage by simply resting (critical glitch on the healing roll) but can keep 'running to his heart's content without his injuries being aggravated by all the exertion.

I'd like to fix this, so how does the following house rule sound?

For each full day not devoted entirely to rest an injured character must make an Edge test with a threshold of the sum of his physical and stun wound modifiers. Failure incurs an extra box of damage to each track that contributed to the threshold. This extra damage is not considered a new injury for the purposes of first aid or magical healing.

Example:

A samurai and a shaman have just dispatched a security team but got hurt in the process. The samurai took 7 boxes of physical and 2 stun whilst the shaman took 3 physical and 5 stun. They press on with the run and are still going 24 hours later. They both roll an Edge (2) test and both fail. The samurai gains 1 physical damage but no more stun whilst the shaman gains 1 physical and 1 stun. Had the shaman rested for an hour or two to drop his stun down to 2 he'd have only had a threshold of 1 but would still have had to make the roll.