I encountered a similar issue on a Simplicity Conquest with a Briggs 18hp engine. In some way, the issue was being caused by a bad air filter. It ran fine without the filter, and runs fine with the new one. However the carb also has some gunk in it still, the throttle wanders until I put it under load (engage the deck). Are you certain it didn't throw one rod? Was there a "clunk" sound when it started running rough? Easiest way to check is by turning the engine over by hand and looking into the cylinder through spark plug hole. I would say fuel issues more than anything, but I can't be certain. Your engine might have a completely different issue than mine had.
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'70 107 with k301 engine swap
'71 106 with 38" deck
'70 147 R with factory replacement k321, 42" deck
'61 Original with 38" timed deck
'63 70 "pinkie"
1863 with 54" deck
'46 Farmall H, '50 Farmall Cub
105 x2 (parts)
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