The reason it is dying at about the same period of run time is because your valve clearance are too close due to block warpage from overheating/wear etc.
As far as repairing this block, forget about it, it is toast. If you go halfway down the slop is greater than .030, as cylinder wear
is never even going down the stroke, and you will just be wasting time and money messing with it any more.
A shortblock is a possibility, but the carb is likely worn out, and dirt probably flows pretty freely through the throttle/choke shafts.
Just check out the engine warehouses online, and they will set you up with a new engine, but putting one on an old cone drive Dixon, that is another discussion, personally, I would look for another mower.......
