Please do NOT use bleach or bleach-based products on the canvas and vinyl portions of your PUP. While it may kill the spores at the surface level, it will not ultimately remove all of it, plus you have the added but more serious issue of accelerating the deterioration of the vinyl. The mold will be more likely to return since bleach does not penetrate into the material as deeply as mold does.
I have used
Iosso Mold and Mildew Stain Remover with great success. It is designed to work on these materials without damaging them. Without the odor issues of bleach, it is safe to work with in enclosed spaces. It is biodegradable and non-toxic.
It has worked on my vinyl awning and the interior side of my previous PUP's vinyl, which is what you have on your PUP.
You might be able to find Iosso locally but I had to order it. I don't recall if it was from the link above. I don't know if it will work on the grease but I haven't used it for that purpose and can't verify it personally even though they claim it will.