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The torque converter is a very likely cause for the symptoms you have described. When the torque converter clutch chatters it will cause a vibration that feels like rumble strips, that is often how I describe converter clutch shudder myself. When accelerating while the converter clutch is still on you are obviously adding more load and this would be a prime time for it to shudder if it was going to.
One thing that I would do is ride with a scan tool attached and see if the converter is in lockup when this happens. If so, try pushing the throttle hard enough that it unlocks the converter or try tapping the brake pedal to try to unlock it, and see if it goes away. If it goes away when the converter unlocks then it's likely the converter.
Converter clutch shudder can be caused by the converter itself or sometimes a fluid issue will cause it. If the fluid is incorrect or there are additives in it then that could cause it to shudder. Flushing the trans using the correct fluid may help or take care of it, but it may need a converter.