If it is a Nikki carburetor, more prone to have needle and seat and tiny o-ring problems, therefore leading to fuel getting into cylinder and mixing with engine oil. I hate Nikki carburetors.
Other possibilities:
Battery is weak and on the way out.
Voltage drop due to corrosion and bad electrical connections.
Starter is borderline and on the way out.
Armor All won’t help that much. If you are storing the mower outside and the sun is beating down on it all day, the tires will suffer long term, as a result.
Never heard of that Kohler model number (double check if correct). What made you use a multimeter to check ignition coils? Did you take them off of mower to check? Did you pull kill wires or spark plug boots to coils and plugs to see if any change in power? Sounds more like choke on...
The maintenance on a gas mower really isn’t a pain. What is painful is replacement cost of batteries in equipment after say 3 years. What is painful is people throwing out 3 year old equipment because the batteries cost too much. I could go on, but that will work for now.
Hunting and surging indicates lean condition. Either you have an air leak around carburetor intake, or carburetor is still dirty (most likely). Definitely drain old fuel and blow out tank, may have a little water in fuel, old fuel, debris.
If an engine refuses to start (regardless of brand, etc.), one of the first things you can check is the spark plug. Is it wet, dry, condition, gap. Then put a little gas into the spark plug hole and put plug back in and see if it fires.