Not transmission noise. There is something going on with the TOB. It may be that one or both of the retaining clips isn't engaged properly. This allows the TOB to be kicked away from the fork and can cause some slippage. The chirp should not be happening.
If it was mine, I'd drop the trans and inspect.
The shudder is going to happen with a stiff clutch. It's sad because that hammering is transmitted through the rest of the driveline. Feel sorry for the poor transmission, diff, CV joints
