After many different attempts to get the wrinkles out of organza tablecloths (ordered from LinenTablecloth), which included: fabric steamer, fluffing in dryer, washing then hanging or spreading to pull out the wrinkles, ironing (with steam and without)....none worked. And, the steamer melted a bit of the fabric.
However, here is what worked for me:
Wash about 5-7 at a time on delicate, pre-soak (or whatever setting, just to wet them/spin out water).
Set iron on mid-heat, no steam
Take out one at a time (leave others in washer to stay wet)
Spread over large table, but keep the part you haven't ironed yet rolled up so it stays damp.
Move quickly and iron while wet. Pull the ironed part to drape over the table so you can unroll a bit more and iron that section. Keep wet kitchen towels ready. The fabric will dry very quickly, and this only works if the fabric is wet. Place wet towels over any stubborn wrinkles, then move and quickly iron. (on some big creases, I ironed on top of the wet towel, then again when I moved the towel)..
As tricky as this sounds, once I figured this out, they ironed beautifully and quickly! I then hung them on a large linen hanger (from the dry cleaner). Hoping they will stay unwrinkled until the reception!!!
Wanted to save others the frustration!!