Strategies for de-wrinkling tablecloths?

So, like many of you, we bought tablecloths from linentablecloths.com (the "economy" polyester ones), because they are like 4000x cheaper than renting. Trick is... I'm really not sure how to de-wrinkle these things in a time-efficient (12 days left! AGH!) manner.

I tried putting them through the washer dryer and it did not budge the wrinkles AT ALL. I could try ironing but good lord that would take forever. We could buy a garment steamer, but even then I'm not entirely sure how to go about it.

We've got something like 30 tablecloths of various sizes and shapes to de-wrinkles. We also have to transport them from our apartment in Boston down to Narragansett, where our wedding will be.

Any tips?