You might consider and oil and filter change using full synthetic or synthetic blend oil. !0W-30 is what is commonly used.
You mention the O-rings on the jets not looking too good. They need to be replaced.
If a cylinder were cutting off due to a bad coil, you would not have enough power to mow, maybe just enough to drive the rider some.
Stay with the original carburetor as long as you can. Aftermarket carburetors are a crapshoot, and it may take a couple of tries to get one that works properly. Just because the advertising says they will fit, does not mean they will work.
If you are not familiar with carburetor cleaning and overhauling, there are many good videos online. Teryll Fixes all, James Condon is really good and Donyboy73