Don't get too pessimistic yet. It depends on how much "topping off" was done and how hard it was run with too little oil in the mixture. The engine will shut down when it overheats, which may have been caused by too rich of a gas mixture, or any number of other things. What is needed is a good and accurate compression test. Have a fully charged battery, remove all the plugs, use a screw-in compression gauge, and crank the engine over at least ten full rotations for each cylinder. Write down the compression on each cylinder. Compression needs to be in the proper range (which you will need to look up) and all cylinders must be within +/- 10%.
If that passes, then your rings are good, and about anything else is fixable. If the compression test is marginal, then run a concentration of SeaFoam or Yamalube Ring Free through the engine IAW instructions.
If you try the SeaFoam, in a separate small tank, mix the 3 parts gas/oil mixture with 1 part SeaFoam. Warm up engine, then connect the mixture tank to the gas line. Run engine until is burns out the gas in the carbs and starts drawing in the mixture. Let it run for about a minute. It may stall out. Let it sit for 15 - 20 minutes, then repeat the whole process. Expect to see a bunch of smoke and black soot being blown out the exhaust. That process will de-carbonize the rings and top end, and will also clean up the carbs.