This get asked all the time, and it's a fair question. Synthetic will give some extra protection over "most" conventional oils, but that difference is hard to quantify. Then you add to the quest for "best protection" and that brings up the crux of the issue.
If a $4 a quart protects you engine just fine, then what is the value of extra unneeded protection? I mean, if conventional oil would give you 3000hrs on your Kawa engine, and syn would give you 3050hrs, what is the advantage? In the real world, we'll never know.
I think you have the right approach, you have it on hand, it's great oil, and fits the use, so why not use it. To be honest, if I had a car to use it in, that's where it would go, and I'd get some HDEO for the mower. If we change oil regularly, in a car or a mower, and maintain it otherwise, oil selection is getting to be a non issue. All the newer oils (with the exception of "fly by nighters" and scammers) are that good.