"I can hear the valve moving when I move the transmission cable by hand."

I take that to mean you disconnected the cable from the throttle spindle to pull it out all the way and let it snap back. Otherwise you shouldn't hear much in the way of sounds unless it is badly misadjusted or the cable is failing.

To expand a bit on what's in the FAQ, the kickdown cable is attached to a spring loaded pawl in the kickdown chamber. With the cable installed on the throttle spindle (and the throttle linkage rod adequately adjusted), when the cable is plucked (lifted all the way and then allowed to snap back down) the spring loaded pawl drops down and may strike the bottom of the valve chamber and make a faint thunk/click sound. If there's grunge in the bottom of the kickdown valve chamber then you won't even hear that. If you've got the cable disconnected from the throttle spindle you may hear a noise when you rapidly pull it out to full extension and hear the sound of the pawl hitting top of travel. When properly adjusted, the pawl should stop just short of hitting the bottom of the chamber when released and you shouldn't hear anything. The only other sound I can imagine hearing is a worn cable making a slight scraping noise inside the cable sheath.

I've gone back for a quick look at your shifting symptoms. The kickdown cable could certainly be related.

First off, check to make sure the cable is properly seated in the throttle spindle. I've had symptoms very much like yours just because the cable had accidentally jumped over into the next slot during handling. This can occasionally happen when you've got a sticky/worn cable and when releasing the pedal the cable goes slack enough to jump over to the next slot.

Second, exercise the cable and check cable integrity as best you can. Make sure the cable is easily snapping back when released both from full extension and when just pulled out a little, and that the cable doesn't stick or change resistance when being slowly pulled out and slowly released. That would be a common sign of internal cable wear and the cable beginning to fail. Even if it runs in and out smoothly, the cable may be just starting to fail. That may actually agree with your symptoms. When you boot the pedal to the floor, the remaining strands in a badly worn or frayed cable can stretch, enough so to make a noticeable difference in subsequent kickdown behaviour. One day you'll boot it to the floor and the cable will simply snap -it makes for a very interesting driving experience of up and down shifting, or more specifically the lack thereof.

No matter what, your tranny is probably overdue for a good flush. I'd do that before continuing as it can affect so many things such as sticky valve balls, overdrive solenoid and the kickdown chamber. Unless the trans is horridly grungy through neglect, a thorough double flush at the trans cooler lines at the rad (fully described in the FAQ) may often be enough and is all I've bothered doing in the past twenty years. Flushing at the trans cooler lines is far easier and less messy than draining and removing the trans pan to wipe it clean and clean/replace the filter. It also avoids issues such as removing a stuck cooler line and dropping cross members. Volvo no longer suggests replacing the trans filter and screen at specified mileage intervals, it can usually be adequately kept clean through regular flushing and/or manually cleaned as needed.

Procedures for checking, adjusting and replacing the trans kickdown cable are thoroughly described in the FAQ.
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now

Thanks for the response. I will check the tranny cable out closer. I did not have to remove a cooler line or cross member to drop the pan, just the fill tube. I figured at 187k it was time for a filter change.

I will check out the FAQ on doing a flush. I also read about the check valve wearing down and allowing bad transmission performance. But I will start with the flush as suggested. Maybe it is just time for a new cable as well.