I've had 2 ankle re-co's so I know where you are coming from.
I previously had the K-Swiss 7.0 Preventer, this was a brilliant shoe. Since then however I have had to go for the ASO Ankle Stabilizer brace, which I have found to be the best combo of support and comfort, as I also used it for Badminton as well, rather than taping my ankle.
For now I have been using K-Swiss Big Shot light 3, as its also a bit wider in its fit, but will also work with this brace.
Its been a while since I have seen anyone make a try 3/4 cut tennis shoe, and even longer since we have been able to find any here in Australia