My son is exactly like that! He is now 2.5 and I registered him for soccer class and that at least that made him tired and seemed to calm him down. Once I saw that, I registered for another class during the week, so we go on Saturdays and Wednesdays.
I'm also planning to sign him up for ice skating lessons once he turns 3. If he likes it, I hope this will have the same effect as soccer. For the sensory issues, I would just encourage any manual work like clay, squishing glue out etc.
Oh, we take soccer with tots soccer lessons with Kids Pro soccer, and planning on ice skating with Kettler ice skating ring as we are in Arlington. Good luck!