I am not exactly sure how best to help, but one thought came to mind..what about building a raised bed for them?...You could control the quality of their soil that way and have adequate drainage....you could plant them shallow under a light layer of mulch, and if any topsoil washes away, more can easily be added...Just a thought....GardenLove

You may want to try planting them in a raised bed that has been amended with organic materials such as peat moss, compost, well-rotted manure, fish meal or alfalfa meal beneath the root. Compact soil around roots. Sounds like you have no problem with full sun. If the root is too large, more than 3 years, I would divide it. Sometimes, your local nursery or local master gardener can help you with that. Make sure you have good drainage. I recommend fall planting or transplanting. Make sure the eyes are not more than 1-2 inches below the soil and work some bone meal into the soil beneath the root. Peonies prefer organic fertilizers so try to shy away from synthetic ones.
When the weather is hot as you stated, try to water your peony thoroughly at least once or twice a month. Too much water will cause your root to rot, too less will slow down the growth of your peony. Never allow the manure to touch the roots. Instead, to feed, put it around the base of peony plant about 10-12 inched from eyes. Each fall, after the 1st week of September at least when it is dormant, cut your herbaceous peonies to the ground being careful not to damage the eyes. I would mulch in the winter, but remove the mulch at the "beginning" of spring. Happy flourishing in the spring!!

You posted in July and I'm wondering what steps you might have already taken to try to get those un-bloomers to right themselves.

You could, if you haven't already done the whole job, instead of raising the bed, raise the plant...an inch or ?

This is often done because it is so simple a remedy to try.

Just go outwards from the plant with a spade or shovel. Dig straight down....and repeat this on all sides.
Pick a side and go under the plant with the spade and lift.
Hold the plant in the raised position and back fill, then firm up with fingers. This is often exactly what the plant needed.

I'd also suggest you stay away from anything that abruptly changes your soil's pH to the acid side. Peony likes it slightly alkaline.

This is not to say you should not use peat moss in making your soil around your peony more loose and able to hold moisture. Peat moss is not heavily acidic...although it is suggested to be part of the mix in acid loving plants...oriental lilies come to mind.

I would also suggest lifting out your peonies with a shovel and reposition them in a raised bed. It did wonders for a bird of paradise that had been sulking in our yard (heavy clay amended with potting soil, manure, and peat moss)--it started growing a month or two after transplanting and have caught up with a larger plant that was bought recently.

A raised bed is fairly easy to construct--we constructed it out of cinder blocks, dug up the soil inside the bed, add it potting soil, peat moss, compost, and playground sand, mix thoroughly, pop plants in, and cover the tops of the cinder blocks with cap stones.

I just popped in 2 bareroot peonies in this bed about 2 weeks ago, and they're putting out shoots, so no complaints here....

Lil