How to deduct $2700 of non-cash charites and not get audited?

I moved from Michigan to Florida and had an estate sale to get rid of most all of my household items so that I didn't have to pay for moving it down to Florida. The stuff I didn't sell which was a lot was donated to the local women's shelter. I know you up the odds of getting audited for non-cash over $500. What backup do I need for about $2700 of current value (not what I originally paid) of items that the women's shelter came and took. I donated items such as leather couches, sterns & foster beds, rugs, lots of new nice womens winter coats, lamps etc..... sure appreciate your advise in advance.