I see. I think a good quality (not the cheap imported stuff) with 6-7 wraps should take the sun light and heat but, like any silage, you can't have damage and let air in or you are going to have a slimy, mouldy mess, as you discovered.

Ideally baleage should be wrapped within a few hours of when its baled, as my neighbor with the wrapper stresses to me. And should be a bit higher moisture than 30%. I've had better results with bales that are wetter than drier although 35% should work. We wrapped some that must have been about 70% this past late spring. Very heavy bales. But turned out well. That is what is pictured in my recent thread below. Cows love it.

Around here most folks use the Sunfilm Gold plastic wrap which stretches, seals and holds up well in sunlight.  But you need to address the mouse and varmint holes somehow. I've had a couple varmint holes on top of an inline tube but seal them up with a special tape for the job as soon as I see them. Minimal loss.