is it possible the problem is with your rim? That is thatthere's something sticking out of it that cuts the tire when you put a lot of pressure on one spot? Or is it possiblethatthe joint of the tire is expanding when you ride off of or onto curbs and that joint expansion then "bites" the tube giving it the characteristic snake-bite punctures?

You might want to try this. Ride your bike to one of the curbs you ride up and over but stop at the curb. Get off the bike and push the front wheel har against the curb. look at the deformation of thetire and how much/little tire is left before it bottoms out. i've done that with a number of people's bikes thereby showing them how little air they actually have in their tire.

As others said, technique is critical. You can actually chafe/cut sidewalls of tires by riding up and over curbs on an angle because the tire slides a bit along the curb.

If i ride up over a curb I pull up on the handlebar just as the front wheel touches it and that lifts the front wheel up onto the curb and then when the rear wheel just touches the curb I stand and throw my weight forward thereby lifting the rear wheel up and over the curb too.

Cheers