(note: I tend to run in minimalist shoes, and at times have used racers for all mileage with no adverse effects)
I don't think "minimalism" is a great solution for most runners. There are certainly advantages (less cushion = more impact response from the ground, forcing your feet to adapt to a proper strike). But you cannot strengthen your feet to fix overpronation. Quite simply, overpronation stems from the ligaments and bone structure in your feet. This is something you are born with, or end up with due to wear or injury. No amount of strength can fix ligament and bone structure. You can compensate a little with the right exercises, but you will end up using tendons/muscles to do the work of ligaments. This is usually not a good solution.
If you want to try "minimalism", read up and do your own research. Read both sides of the argument, as letsrun often posts a very biased view.
PS: The DS-Trainer is an awesome feeling shoe. Can't hurt to get a pair and try them and see how they work. It would be a bit of a shock to the system to jump all the way to the DS-Trainer from the Kayano... perhaps your next shoe should be the 2140, then get the DS-Trainer the next time. Or get the DS-Trainers and wear them every other day. Everyone will react differently to new shoes, listen to your body, it knows better than posters here.