Rubbing noise on takeoff with 1992 190E 2.3

Hello folks,
I have a '92 190E 2.3 with 170k miles. I'm hearing a short, loud rubbing noise from the rear of the car when starting from a stop. It sounds like someone is scraping the underbody of the car with a
screwdriver handle. It happens in the first several seconds of the movement, and never during driving.
I have some theories as to where this is coming from; I'd love to hear your thoughts on what it could be.
1. Bad differential. I know mine ran dry due to a leak, and whines at high speeds. However, it's not a LSD, so there are no clutches to rub, and if the noise was caused by skipping teeth wouldn't it happen during driving too, and sound a little different?
2. Bad transmission. Maybe the clutches inside the auto tranny are somehow worn out and rubbing under high torque? Still doesn't make sense to produce the noise only on takeoff.
3. Driveshaft rubbing against something. Could the high torque on startup cause something to flex and touch the driveshaft?
Cheers Alex
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Two things to check. Is the handbrake releasing at the wheels? Flex disks in the drive line. You can inspect the rear easily .......the front requires removal of the underbody shield. Peter.

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Thanks for replying! I don't think it's either of these though. I use the handbrake often, and it doesn't seem to have any issues. I also changed the front flex disc recently, and it is solid.
I'll inspect the driveshaft for scratch marks next, including under the exhaust shield.
I guess I am mostly worried that the diff or transmission is at fault, because it's a more complicated problem than something with the driveshaft.
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