Put the wrong gas in my mower, am I fucked?

Yea, that happened. Instead of the 93 I put in it, I put in a mixture of oil + 93 that was for my 2 stroke bushwacker lol. It took at least 3/4 a tank of this bad gas. I forgot they were mixed. So I mow half the lawn, and it finally dies, and I can't start it up. Once I figure out that I put the wrong gas in, I dump all that gas out and unhook the fuel line that goes to the carb to drain it completely. Then I fill with premium 93. Now I can't start the mower, so I take off the air filter and start gently putting very small amounts of gas (like a few drops) directly into the carb, and that continues for 10-20 minutes. It's still sputtering, but I can keep it running as long as I'm doing this. After about 10 minutes of this, the mower starts running like new. It's not sputtering, and runs fine for 8-10 minutes at the normal RPM. I was able to cut some of the lawn and no problem. Then all of a sudden it starts sputtering again and eventually dies. I can start it up, but it dies again in 10 seconds or so. My next step is to clean the carb, anything else that needs to be done? Am I fucked here? I mean, I have a full tank of fresh 93, I emptied the fuel line, and got it running for 10 minutes and cut some of my lawn with it, what could possibly cause it to cut out after that!?