First, are you asking about wrapping or twisting? Those are two different things. By body tube section are you talking about the fin can, or the payload section?
Your diagram shows the line from the fin can wrapping around the line holding the drogue. If that is what is happening, I assume the fin can is spinning in circles around the payload section and that is causing the wrapping. This is unusual because usually both will spin in a circle together and one won't wrap around the other. I would try a larger drogue to ensure more separation between the payload and the fincan. Keep the line between them taught and that should prevent the wrapping.
If the tangling is caused because the line between the fincan and payload is being twisted excessively and the other line is being caught up in the twists, then a swivel on the fin can is probably your best solution. My experience is that only ball bearing swivels work well, the non-ball bearing types just don't work. I have one rocket where the fincan will spin at near 100 rpm on the way down. With a good ball bearing swivel on the fincan, there is no twisting of the tubular nylon shock cord.