When I've heard of idle climbing like that as the engine warms up, it was the ECT. That could be your entire problem. As it warms up, if the ECT goes to an open condition then the engine races, exactly as for you. A failed ECT starting out at an incorrect value thinking it's operating in sub-freezing conditions would set the base idle around 1,200-1,300 rpm and it would go up from there, again as you describe.

I've always wondered when forcing limp home mode (by disconnecting the AMM), just how many sensors are ignored. Naturally, it ignores the missing AMM signal. All I can find in the service manuals is that it defaults to a rich fuel mix map, meaning an extended injector duration. My understanding from elsewhere (and as I recall from my own driving experience in limp home mode) is that rpm is governed, or perhaps the fuel map is so crude that a rich fuel mix at lower rpm becomes a lean mix at higher rpm, making the hesitation I witness being from fuel starvation.

What I'm wondering is if the ECT is also ignored (possibly even the O2 sensor). The engine could certainly start, idle and operate half-decently not knowing the block temp. With that thought in mind, if you force your engine into limp home mode (disconnecting the AMM before starting) and as it warms up the idle does not start to race again then that would be proof that the ECT sensor is ignored and that your ECT was faulty. Maybe worth giving that a try to see if it confirms my theory.
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now