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?