Another one who could have written your post when DS was four.
It will get better - in retrospect, it appeared to me that four was the age when DS found the combination of social overstimulation as intellectual under stimulation hardest to handle. In order to cut down on the overstimulation, we tried to keep our days to one activity, max - and one of those was preschool. I also read up a lot on sensory issues. check out sensational kids and the out of synch child and see whether some of it resonates. Hard work (pushing boxes etc.) and sensory stuff like water and mud play helped regulate our child, running around like crazy during recess did not - a lot of physical exercise just serves to ramp up their excitement and getting tired makes it harder for them to compensate, so conventional preschool teacher wisdom on this May not help. If you feel that sensory issues might play a part, a round of OT might help (it also might help to get preschool teachers off your back, who like it when parents demonstrate a willingness to look for outside help.
There is probably not much you can do help the intellectual under stimulation. What we did was simply tell his teachers - they did believe us and it helped them put some of his behaviours into perspective, and even if there wasn't much they could offer, reframing his behaviours helped them and thus helped DS. It might not work for every teacher. Tread carefully on that one.

Maybe they also need some perspective on what is normal excitable behaviour for a four year old - they may draw from a very select cohort for their high quality preschool. I remember talking to DS music school teacher about whether he was as much of a behaviour problem as in preschool and he said, sure, he was a handful - but mostly so in comparison to the exceptionally well behaved older girls in his class. Then added: "you know, I teach in all parts of town, you don't even know what a real behavioral problem looks like!"