My first thought would be to build the deck in individual 4x8 sections. So you build a frame out of 2x4's or 2x6's with one sheet of plywood on top and the insulation pre-installed between the framing members.
You would then set up your concrete piers and beams that would support the sections. If you use 2x4 framing for the pre-built sections, you would need more beams and piers, but the individual sections would also be lighter and more easily man-portable. Place the pre-built sections on top of the joists and screw them together from underneath.
When you disassemble, you just unscrew the pre-built sections from each other and the joists, take them out in one piece, and stack them on a trailer. Being 4x8, they are the perfect size to fit in just about any trailer or pickup truck and not too heavy for one or two guys to handle. Once those are removed, you can disassemble the beams and piers.
Site-built deck drainage
Here is an article in Fine-homebuilding on site-built deck drainage.
In this article they use EPDM rubber roofing material.
I wouldn't hesitate to use this or creative alternatives, but I wouldn't consider this as a "waterproof/roof" system. I would consider it rain-proof where it diverts rain and rain-runoff from underneath the deck.
Retail deck drainage
There are products available that are designed for this as well. Like Timbertech Dryspace for example.
My opinion
Using either a site-built or retail product, I still wouldn't store anything under there that would be ruined from getting a little bit of moisture now and then.
If you want a real waterproof roof, then build it as a code-approved roof with code-approved materials installed how they were intended to be installed.
Issues
One potential issue I can think of right off the bat is that dirt and debris will collect in there, so do you have a plan on cleaning this out? You will need access from time to time to at least stick a hose at the highest part to rinse it out.
Another potential issue is that this would limit the airflow and potentially increase the humidity between the decking and drainage material. This could contribute to things like cupping or premature finish failure on wood decking.
Real Roof (info as requested in comments)
60mil vinyl can be considered an approved roofing surface. You would use something like this if you are not putting another surface over the deck.
Another roofing option (if you wanted to add wood planks) would be to do flat roof (i prefer a torch-down roof): then build panels out of your deck surface, or attach the decking to sleepers (see image below), or use wood tiles
Best Answer
Indeed, sistered boards may provide an area that is vulerable to moisture buildup and decay. However, in practice/experience the effect is not very pronounced. If I was concerned about it because of general moisture in the area, then I would use zinc paint between the joists to help reduce any mold issues.
If spacing is preferred, then I'd recommend a 1/8" space (similar to the space between roof sheathing/plywood). There might be some kind of special spacer, but chances are, it's a rare and unpopular product. You could potentially use washers, but that could be tricky unless you use bolts (I would want the nail to go through the washer to keep the washers from falling out).
Another way that this could be accomplished would be by using steel or aluminum shims. I would just cut my own from a piece (or three) of 1/2" x 1/8" steel or aluminum stock... maybe 6 foot long, and use 6" strips as spacers.