https://www.ebay.com/itm/401148578866?hash=item5d66518c32:g:BVMAAMXQuTNTPLJxif it was run hot repeatedly the coil could have been heat damaged and your description sounds like the carb is loading up the saw with fuel when returned to idle. 45ish bucks for a coil and about the same for a aftermarket carb I would just do both and move forward for under 100 bucks. I have seen carbs destroyed by inexperience many times. It only takes one oopsy to ruin needles/seats/ jet bores/ jet seats/ jet tips or totally muff up welch plugs resulting in cross leaks etc. triple check my parts posted for being correct as my wife reminds me often that I am wrong from time to time.
https://www.ebay.com/itm/283812579236
https://www.ebay.com/itm/283812579236