[Nonfractal]

A main source of shuddering is flexibility in the motor to axle alignment.

I see you have put a short can motor into a long can motor mount.
If the motor is only anchored on one end , this is asking for the kind of behaviours you describe.

Shims are available on thingiverse for 3d printing.
The shims will anchor the motor on both ends and also help to centre the weight of the motor in the centreline of the chassis.
A small dab of epoxy at both ends will ensure that the shims stay in place.

Below is a pair of shims anchoring a Slot.IT MX16 S-Can motor into a Black Arrow motor mount