Listen, the correct and only way to check your bore is with at least a dial bore gauge and set of mics. Since you will likely not own these, it is best to allow a pro to check the bore dims. Feelers and "checking slop" simply are not good enough. I would bet the bore is worn out and you may have installed new pistons in a worn hole when they broke. I would say, with most certainty, that a fresh bore and set of pistons will fix your problem. The rings are no indication of piston wear whatsoever and if you intake ports are not chamfered, it can cause skirt damage but will rarely break the piston. This looks like a classic case of "worn out bore".
Brandon