The fact that these spices are absorbing enough moisture to form into hard bricks suggests that they may also be damaged by the moisture. So regardless of the brick problem, we probably need to be storing these spices and any herbs in truly moisture tight containers and using a desiccant with them to keep them dry.
I've always thought that the containers that most of these bulk herbs and spices come in are not very good. They don't seal at all. So as Steve suggested, they could be transferred into appropriately sized mason jars, which will make a good seal as long as you carefully wipe any powder off of the jar's rim every time before you replace the lid. Anything that contaminates the interface between the glass and the rubber seal of the lid will create a leak.
You can also pull a vacuum on the Mason Jars with an attachment to a vacuum sealer.
Something else to consider when storing any food long term is the use of an oxygen absorber. A lot of the degradation of foods is due to oxidation. Removing all oxygen from the environment will preserve the "freshness" of various foods better and give you a longer shelf life.
So this works well, but it's extra work all of the time.
I often have use for desiccants, and have found that DrieRite is hard to beat, especially for price.
The stuff is FDA approved and food-safe. I like the bags that they sell. You need to store the unused ones in a sealed container, of course.
If you put an appropriately sized desiccant bag in with the food in question, and seal it in a mason jar with a clean lid/glass interface, that should do the job.
I'm fortunate that where I live this isn't a problem because it's so dry most of the time. But I do sympathize!
Also, keep in mind that ziplock bags are not moisture tight. Water vapor and food smells can easily pass through the plastic. Even foodsaver type bags may not provide a complete water vapor barrier (but they're far better than a baggie).
The aluminized Mylar bags used for storing freeze dried foods DO provide a vapor barrier due to the aluminum layer. But you need more heat to seal them properly than what you get from a typical foodsaver type machine. Typically, you need a device with an adjustment for the length of time that the heater operates. I find that the clear foodsaver bags usually require a heat impulse of around 3 seconds, and the 7 mil aluminized Mylar bags I like take about 6.5 seconds with both of the sealers I've been using.
Something to consider would be to repackage the large quantities of spices into smaller aluminized Mylar bags with O2 absorbers so you aren't opening a large quantity at any one time.
It would be neat if someone sold various spices in bulk, but already sub-packaged into smaller, well-sealed aluminized Mylar bags so you could open up an ounce or two at a time. But I suppose the price per ounce would naturally be higher than what we pay for the big bulk containers of these spices.
If you think Colorado is dry, try Wyoming! ;)