I will probably have the same problem.

Will spacers move the tire away from the fender?

If you deflate the tire, will that help?

Maybe you will have to use a smaller diameter tire that fits the wheel and mounts properly?

One of my trucks with a side carrier came with a different size/brand used spare tire. I thought it was cost-saving measure - maybe it was a necessary measure in order to solve the problem you are observing?