Glad the starter issue is behind you. For future reference so you don't get stranded, if the starter won't catch because of a dead spot in the windings or a sticky solenoid, you can often get it to catch by rapping hard on the starter motor a number of times with the end of something like a 2x2. Some mechanics will even get underneath with a hammer and beat on it. When I first encounter starter motor problems I start packing a 2x2 until I have time to replace the starter motor. On more than one occasion when out shopping and it wouldn't crank, I'd simply pop the hood, do a quick Fonzerelli on the starter to teach it a lesson, then now being able to start and drive home. Really impresses the passengers and bystanders.

Trying to think of more basics for you to check, based on what you just said about 400-500 rpm when still warm after sitting, I'm starting to wonder if the TPS on the throttle body could be on the hairy edge of being out of adjustment.

If the ECU doesn't know it's supposed to be maintaining idle then depending on how open the throttle plate is at rest and where the IAC valve is floating then your base idle without the ECU trying to adjust it may be down in the 400-500 range and it will indeed stumble and stall at that speed, even for an otherwise normally running engine.

With the engine warm and left to sit so it stumbles, shut it off without touching the gas to feather it out then check the TPS for an audible click as it moves away from the stop when opened by hand. It should not be set on the hairy edge of clicking, which is a distinct possibility with your symptoms. It might be clicking normally when cold, but when warm and allowed to sit may no longer be in proper adjustment. There is a spec inserting a feeler gauge at the stop screw where it's still supposed to click. A strip of cereal box paperboard inserted at the stop screw should still give a click when the throttle is opened. With the throttle normally closed, the throttle spindle (cable pulley) should not be up against its stop (otherwise the linkage rod needs adjustment). The throttle cable should also be checked to make sure there's a bit of slack.

Beyond your immediate stumbling problem, thinking of basics in general for a recent car acquisition, I wouldn't assume someone hasn't been fiddling around with the throttle body in previous years. I always start with a thorough throttle body cleaning on the bench (including the little vacuum port holes), checking the centering of the throttle plate, then properly readjusting everything to Volvo spec: the throttle stop screw (1/4 turn method, drop of paint so you'll know if someone ever touches it again), the TPS (click with the spec'd feeler gauge inserted, also different procedures for Bosch and VDO switches), the linkage rod to adjust the spindle stop gap, the throttle cable slack adjustment and kick-down cable adjustment (adjust to just before the pawl clunks against the bottom of the kick-down chamber down in the trans when the cable is plucked)). Double check that all electrical connectors (TPS, IAC and AMM), are clean and protected from moisture with dielectric grease, then fully seated. Make sure the flame trap is clean and the oil separator box isn't plugged. Tap solidly on the IAC with the end of a wood stick after it's been idling a few minutes during warm-up to see if the idle changes, indicating a dirty/sticky/worn IAC. With the engine idling, spray water (or starter fluid) around the throttle shaft to check for any change in running to indicate excessive wear at the throttle shaft. Inspect the accordion air intake tube carefully for splits, especially underneath. It all adds up to help with better engine operation and minimize the number of possible problems down the road.
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now