"So far, I have observed no glitches using headphones plugged into the computer. The Tascam has 2 headphone jacks which I have not yet investigated."

Two items come to mind:

You should test headphones on Tascam, which would eliminate "speaker" issues if the glitch is heard.

I am just guessing here... You can hear audio from computer headphone jack while Tascam is connected and powered on? Running both Tascam and internal Realtek at the same time, or you are unplugging Tascam to listen from computer headphones jack?