I've machined plenty of parts with bearings before, so I'm not worried about getting the required accuracy. The lathe I've just bought should help there too :)

30mm is too small I think, on the drawing currently I've bored the shaft 27mm which does not leave much for the bearing.

How do you tell if the bearing is classified as 'deep groove', or is it somewhat arbitrary? The standard bearings I had selected were the ones with a bigger outer diameter (72mm), though not the biggest. I've got 2 good quality, FAG and SKF if I recall correctly, 45x85mm bearings.

I'm not entertaining a belt or rack and pinion drive so the only other option as far as I'm aware is to tension the ballscrew sufficiently to stop whipping. That does not help with the inertia of the screw though, which for 2000mm is similar in magnitude to the other forces.