As I'm conceiving the next generation ass-kicking artefact-based task management system, I have to make a statement on so-called task priority.

One can argue about the variety of psychological models on the subject, but to me, there's no such thing as task priority in the real world.
A task – sooner or later – is being done or discarded, or better, it starts consuming resources right from its definition, and those resources are real, the time spent is real.
That's why, the only questions how (= when + how much) those resources are spent.
Thus, the most natural thing to do is to define a period of time this task can "wait" – until the next action.

So I propose always to use time-to-action as the basic measure of task precedence.

Of course, deadlines, dependencies, schedule and resource constraints might be additional parameters to the planning equation, but even that basic attribute on each of your tasks is good enough to answer the core question "What in the bloody hell should I be doing right now?"