How long is this spindle? 24 inches or 6 inches? It makes a difference as to where the midpoint is
If for some reason there is no way to improve this design, then put one pair of bearings in the middle and the other pair at the drive end. The further back from the business end that you put the bearings, the more load is transferred to the rear bearings. So to get the maximum stiffness of a poor design, that is what I would recommend.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)