Having an axle bolt “stick out” and locking one side of the drive train on a recent KoP chassis is pretty strange. The plate separation is held pretty constant by a combination of the ties into the end sheets, churros, and those 3x1 top plates, and the shafts are 3/8" bolts with nylock nuts. Once you get those in place, they should be pretty solid under any reasonable amount of misuse. Do you have a picture?
Also, if your robot was performing well before the shaft issue, I wouldn’t change the wheel size unless you compensate with a different gear ratio. If it was accelerating sluggishly or you were drawing too much current, smaller wheels (or a lower* gear ratio and the same wheels) may help with this. If you could accelerate really quickly, but couldn’t get enough top speed, larger wheels (or a higher* gear ratio and the same wheels) may help with this.
As noted above, changing among solid, pneumatic, omni or mecanum wheels is entirely a function of what strategies and tasks you are taking on with your robot.
* A lower gear ratio is one with a higher number, and vice versa - that is, 12:1 is lower gearing than 9:1.