I see the type of sprockets you have are called "speed sprockets" identifiable with the pointed tips. All that they are supposed to do is let the sprocket enter and exit the cleats more cleanly than the rounded end type sprockets. The bottom of the sprocket where the cleats sit will be the same size no matter which type you use and will not effect the "soft spongy" feeling that you say you have. If anything, I would guess a loose track would be your problem, however you say it seems tight. Other than a loose track, I can not hazard a guess as the why it would bind when you push it. There are alot of other members out there that can probably suggest a cure, as thre are many out there that know a heck of a lot more than me (except The Old Trucker).
Good luck Mike.