Two stroke motors are very simple and very reliable even when abused terribly so unless it's been run without oil I'd be surprised if that was the problem. With a modern engine and modern oils I'd stick to the manufacturers spec: too much oil doesn't actually help combustion because it's just more to be burned and potentially foul the sparking plug.
By far the most common problem is dirty fuel, especially water contamination. The in-line filters that some modern engines have block easily even from the condensation that you will get inside a partly full can. Fuel does also go stale if stored even for 12 months: there are some additives but I'm not sure it isn't oil company propaganda.
Air/fuel mix can be an issue especially if it's too lean when the engine will run very hot. You can easily check this by cutting into a reasonably sized log. Off-load the engine should be 4-stroking, making a sort of deep barking noise at full throttle. On load it should change into a smooth scream.
One other place to look is the air filter. If the chains aren't kept really sharp sawdust can block the filter and make the engine run badly, though not in 10 minutes.