I think I may have solved this, but I am confused.

If I go to Preferences->MIDI, and I *uncheck* "Zero Controllers When Play Stops", then behavior is as I desire: Pressing Stop during playback will turn off all notes *and* turn off the damper pedal on my piano.
 
However, this is the opposite of what I thought this option should do. It was previously not working for me because I had made sure that this option was checked.
 
In any case, as long as it's working I'm happy. 
 
 
EDIT:
Ok, I jumped the gun here. That did not fix it. But at least now I am less confused. 

smonahan001
I think I may have solved this, but I am confused.

If I go to Preferences->MIDI, and I *uncheck* "Zero Controllers When Play Stops", then behavior is as I desire: Pressing Stop during playback will turn off all notes *and* turn off the damper pedal on my piano.
 
However, this is the opposite of what I thought this option should do. It was previously not working for me because I had made sure that this option was checked.
 
In any case, as long as it's working I'm happy. 
 
 
EDIT:
Ok, I jumped the gun here. That did not fix it. But at least now I am less confused. 

If the sustain turns off sometimes but not other times then its definitely a midi message, maybe its the other way around, maybe the piano is receiving a sustain message to stay on ?
 
exactly how long does the sustain last for when you press stop only ?
 

Okay, it's not Sonar. It's Pianoteq.

I installed on a completely different machine, and created a new sequence. I recorded a few bars with the TTS piano, and it behaves correctly. Then recorded a few bars on the Pianoteq, and still getting lingering notes. I opened the MIDI option on the Pianoteq plugin so I can see MIDI events as they're coming in. I can see all the notes on and off happening, and the pedal on and off happening. And when I hit Stop, I can see all the channels getting All Notes Off messages... but no controller off messages.
 
I will pursue this further with Pianoteq. Thanks everyone.

Normally if you stop the transport before reaching the 0 cc, it remains affected. Especially noticeable with pitchbend cc's.

BTW, my biggest midi issue is a synth that suffers from stuck note syndrome.