Hm, tough question! The only way I know that you could be fairly sure of having them is to cut them when they start to show color, dip the tip of the stem in wax and put them in the fridge. Since you mention that you don't have fridge space to do that, I just don't know what else you can do. I don't think that shading them will keep them cool enough to hold off bloom that long. My Sarah Bernhardts are usually pretty well shot by then.
Wish I had more help for your queasy stomach :) We're getting a sudden blast of heat, and the peonies are showing it..they're not lasting nearly as long as usual.
Good luck with the wedding, and again, I wish I had a really good, solid answer for ya.

Yeah, I live near you and my peonies (several varieties) are all done by late June. The first ones are beginning to bloom now, and will be done blooming in a week and a half or so. It's possible your variety is very late-blooming, and then you might be in luck, but I think your safest choice would be to cut and refrigerate the buds as flowerluvr suggested. I don't think shading them would help. You'd have to cool them!

Let us know what happens, and good luck!