You'd still need something approximately same length as the extension tube, attached to the rear axle housing and rubber isolated from the car body at its other end. This keeps the pinion angle correct so the U-joints work correctly.
As long as the differential pinion's shaft is reasonably close to parallel to the transmission main shaft, the u-joints will work without vibration.
Then, if one could figure how to attach the u-joint flange directly to the differential pinion at the rear axle, could run driveshaft from trans to rear end. This eliminates bracket, donut and bearing.
Bill