Installed that $15 new lawn mower carburetor from Amazon. I decided that while I could probably fix the old one by simply drilling out the jet, it's a pain to get to it so I took the path of least resistance. The mower started right up and runs fine. I left a glowing 5-star review on Amazon for it.
Years ago I had an issue with the carbs on an old motorcycle that went unused for some time without proper prep of draining the gas or using Stabil, etc. The jets and other innards had gotten "varnished" to the point the size was off and adversely affected the mixture. I was able to clean them up using an ultrasonic cleaner. Not sure if you have one or are aware, but it might be useful for future reference.