My next door neighbors built beds around their peonies without moving them and their peonies are doing just fine - never missed a beat.

I don't know if this would depend on the type of peony you have or not but they had quite a variety growing.

The downside to this is that they offered me some of their peonies and they are too deep to dig out now without digging up and disturbing the entire peony plants and neighboring plants. We tried using spade to just take out a little clump but it would entail going down 8 inches through the bed and then further down (probably another 10 inches) into the original soil. It just can't be done without tearing apart the entire bed and distubing everything. If it were my own bed I would do it but I didn't want to pressure them into something they were not looking happy to do.

So if you think you might be moving them sometime in the future you may want to raise them now at this time to make it easier later.

Adding that much soil on top probably won't kill them, but I would expect that they won't bloom for you again. If they are done flowering you could raise them up to their preferred level of 1-2" below the surface anytime now.
They may sulk for awhile, but at least they'll bloom again.

Kris.....my only comment on Bud's comment about having raised the bed around her peonies and having them bloom....well....I heard once that a flyer bailled out of a plane at 10,000 feet.....without a parachute..... and survived. There is no accounting for just plain dumb luck.

The peony is a plant unto itself....it has this brain that tells it...."I'm planted too deep and I will not bloom".....

You put a peony at a particular depth....and it blooms. Then you topdress it....you bring soil around its base, effectively putting the plant deeper.
Ninety-nine percent of the time, the plant resents what you've done and refuses to bloom...or blooms not as expected.

So, once you have found your depth, leave it there.

If you feel your plant is not blooming as you would like, and think its in the ground too deep....simply lift it.
Dig around the plant's four sides, as deep as you can so that the entire plant is free of the soil holding it. Then choose the side you wish to lift and put a spade or shovel under...and lift. Backfill as you go. Lift it a half-inch...an inch...but try to not take it out of the ground.
Just backfill and firm up....then water generously.

Sometimes this will not in any way harm the position of the roots and may not cost any non-blooming time.