The current Jaycar motor/gearbox ($23.95) should be quite OK to use although the hole in the small pulley will need to be enlarged with a 4mm or No.18 or 19 drill as the Jaycar gearbox has a 4.2mm dia. shaft. This motor is 12v DC and runs at 36RPM so when wired in using the original motor wiring including the capacitor across the motor terminals, the trim pot on the existing circuit board can be used to adjust the table-turning speed. The existing pulley ratio of course means that it should run nice and slow.
As can be seen from the photo below, I simply used a wire twist tie to hold the new motor in place, the wire passing through the original motor mounts. I will replace this of course with something a bit more professional. The original set up has a nylon adjusting screw that pushed the bottom of the motor/gearbox away from the mounting frame thereby tightening drive belt on the small top pulley. I managed to lose the small nylon screw but had a suitable metal replacement (2mm metric bolt I think). The new motor wanted to slip sideways off the tensioning screw so I made a 'saddle' from a piece of brass tube to which I soldered a larger nut, the end of the tensioning screw sitting inside the nut. While the nut can't be seen in the photo a little study will show why it is required. This saddle could be made from a piece brass sheet.
The outcome was a very quiet drive with enough torque to eliminate the turning hesitation (slipping/almost stopping at times when turning) of the original drive.
Here is a video of the drive in action, the video camera is sitting on the baseboard and the drive is under the turntable, you have to listen very carefully to hear anything in the video. The drive does make a little noise in operation but nothing like the high pitched noise of the original.