The amount of force needed to re-draw jacketed bullets is very little and can be handled in a normal sturdy reloading press. In fact it is easier than Full length sizing some cases.
I have done it with home made drawing dies and just using re-sizing lube. LEE sizing lube would be ideal.
The step from .338 to .333 could be done in one pass and should not effect the relationship between the jacket and core.
Corbin recommends no more than .010" re-drawing as, with more than this, the jacket comes loose from the core.
Having a partition should not make any difference at all to the exercise.

I could make a set of hardened die and punch for anyone that wants one, in what ever size.

John, that news that TSE are going to make .333 barrels is really good, eh.

Tony