A faster moving storm is not going to upwell as much water, no, but a storm of sufficient intensity is going to mix water over a large depth. For category 3/4 storms, that is about 70m in depth -- the waters over the central Gulf have not recovered from Katrina to that kind of depth, only to a near-normal value. This mixing occurs regardless of the storm's speed; it is a sole function of storm intensity and its influence on the underlying ocean.

Thus, it's not quite correct to say that because the storm is moving faster than Katrina, the recovery of the oceanic waters underneath the storm is not going to be a concern. It will be a concern and likely a limit upon the maximum intensity of the storm. Remember: Katrina was the exception rather than the norm; most storms do not come close to approaching their maximum potential intensity in the Gulf as a result of two factors: 1) shear and/or 2) upper oceanic heat content. Here, it's the latter that should play a role in limiting Rita's intensity -- likely to a more "manageable" cat 3/4 level than another monster.