you can use clear plastic saucers uner your Smart Pots. Like these:
Saucers

You can find them at your local box stores, in a multitude of sizes.

They would work much better than a tarp.

PV

You can also get feet for under your pots to help with drainage. They are everywhere.

http://the-plant-directory.co.uk/pots-and-saucers/pot-feet-ceramic/ceramic-pot-feet-ball-design-blue-glaze

Anything that causes your deck to be constantly moist will cause premature rot. The plastic sheet is probably as bad, if not worse, than sitting the pots directly on the deck. Bricks would be much more quick to dry, as well as clay saucers vs. plastic saucers, but I wouldn't want any kind of saucers outside, unless they were being used upside-down. The standing water issue you mention on the tarp would be even more of a problem with saucers. I have a wooden box thing with wooden legs that's a planter and I put bricks under each of the legs for this reason. As soon as the sun hits them for a minute, they bake dry.

Pavers might get the job done less expensively - and with less actual pieces to move. Is weight an issue? You might be able to get even less expensive by mixing your own quick-concrete and making pavers. They have different colors available if the "almost white" isn't what you'd want to look at. Probably depends on how many you would need, whether or not including the cost of buying the mold would be a savings at the end. With home-made pavers, you can do more interesting things though, like embed decorative objects or imprint leaf shapes. Something you could also use for stepping stones at some point in the future if you want.

As you raise plants, the increased risk of being knocked over from wind increases also - as well as the distance they can fall vs. just being tipped over. So, as you probably already know, make sure they are not wobbly from your efforts. That's one of the failings, IMO, of pot feet. There's usually 3 which is not enough for stability in the face of a 40-mph wind gust, common here.

While deciding on a more permanent solution, anything free you have or could easily get, like plastic water bottle - or other - lids could be used to help.

Something re-purposed might be an option, like grates from an old oven or grill, wire refrigerator shelves. If there's a junk yard nearby to browse, you might see something...

I have Two large decks with multiple planters on each. I have tried many different things, then out of frustration I put some plastic water bottle & soda caps under them just as a temporary fix. I have used them for years now. You can hot glue them to the bottom if you like. So far I have not found anything that works better. It is cheep, easy and up cycling is a green solution to the problem. Good luck.

Depending upon the size and shape of your pots, you might also be able to consider wheeled pot caddies. Such as : Pot caddy