I am now able to open my package files in TSRW to make sure that there aren't any issues as well as run a vanilla game with only the mod that I am testing. So far I have had 2 submissions rejected due to missing textures. As soon as I had both things installed (and figured out how to set the paths, and open another package in TSRW) I checked out the most recent rejection and it's textures were all there. My vanilla game also didn't have any errors/crashes. So I am not sure if this is going to solve the issue of having some of my submissions rejected. If this is the case I may need to take a indeterminate break from submitting so that I can try to figure out what is going on. I really hope that doesn't have to happen, but I want to be able to prevent this issue.

*For now I've remade one of the rejected mods, started over completely. It would be a happy confirmation if the testing results from TSR are the same as mine. This can be very confusing! To anybody else that is learning as well, don't give up!