No, the oil is only there to protect the piston rings/bore, and the main and big-end bearings. So long as it manages to get through the main jet, it's all good. Since it runs properly with the Zama, the fuel is getting through, and it can't get through without taking the oil with it, or there would soon be a pool of oil over the jet, which would stop the music. So, same petrol/oil ratio regardless of carburetor.
If you need a challenge you could identify the Walbro model, study the manual, and do some experiments Ty. Since meanwhile you'll have the blower working, it wouldn't need to be a high priority project. You might even do the future tests with the Walbro on a different engine, rather than disturb one you may be using for serious purposes. My system is to keep no spare parts, just a spare machine in working order, and then never use the spare machine so it doesn't end up half as bad as the bad one you are testing after a couple of years. That means having now found it's the carburetor, I'd either choose a permanent replacement carburetor and throw the bad one away, or I'd laboriously fix the bad one. Frankly, since the bad one is an emissions carburetor and therefore a pain in the backside to tune, it would be in the skip already.
