Ugh! I feel your pain. I stored clothes for 6 years until I had my second daughter. The clothes had all those big yellow spots and no one seemed to know why or how. I think it's a moisture problem. The attic may not be a good idea.
The space bags seemed like a good idea because they are so air tight, they may be your best bet. Plus you will save a TON of space.
There are some packets called "Damp Rid". I got them at the Container Store, don't know who else sells them. I put them directly in the storage bins but they sell different sizes that will work in a storage closet and other rooms, spaces.
Lastly, I used the hottest temperature possible for the clothes and used oxy clean. Sometimes, if the clothes were white, I would layer oxy clean directly on the stain and add a little hot water to "activate" it.
Also, on pure white, I would take a q-tip, dip in bleach and dab the stain. Have to rinse fast otherwise you could damage the material. you can dilute the bleach. I know that is extreme but as far as I was concerned, it was my last resort and the clothes were ruined anyway with the yellow spots.
Lastly, my mom has a method that works on a sunny day...she put salt and lemon juice on stains, let it sit in the sun and it works. I am not sure if she only did it on white but it works!
Good luck.