Dry air is the best treatment for this I suspect. Maybe get them out of the box and onto a rack, or hang them? But ultimately, if the environment is too humid that may not be enough.
I've always cured mine indoors and had no problems - but I've seen what can happen in a cool damp shed, and those less ideal conditions can be lossy.
If you can't bring them into a warm dry place with good air circulation, I'd be tempted to speed up the dry down process by cutting off the greens, maybe leaving a foot or so to reduce the risk of fungus getting down into the neck, trim the roots to an inch, and get them onto some kind of rack where they're not touching each other, maximum air around them.