I'd need to move my small collection along with my other belongings, which means that they'll be in unfriendly, extremely humid air conditions for about a month. I was thinking about putting the whole album in a thick cardboard box and putting it in a plastic bag which I will tie shut, however I'd prefer to hear your advice since I fear the cardboard won't ve enough to get rid of humid air and I might still end up with them sticking to the album.
That would be packs of silica gel, which come in bigger packs than what comes in food packages, etc. So unless you have a big hoard of accumulated tiny packs, a couple 25 gram packs in the plastic bag containing the album works. Then into the box with more packs to keep all as dry as you can. It's good for storing tools the same way, too.
Definitely buy bags of dessicant or silica gel and add them to each box. That will help a lot. One popular brand is "Damp Rid" which can be purchased in packets or large bags. Note that te bags you put it in must be breathable so don't put it into plastic baggies. That won't work. I save every silica packet I ever see. Often they come with packages or clothing or whatever. They all go into a shoe box for later.