tree peonies

I have a small tree peony about 5 yrs old. I'd like to dig it up and give it to someone who might enjoy it more. It hogs space and has weak limbs, perhaps because it doesn't get full sun. It's grafted and in the spring sends up shoots from the roots which I know rob it of energy so I remove them. I've heard TPs resent being moved. Do you think I could dig it this fall and overwinter it potted (as I do herbaceous garden peonies). If so, would potting it more deeply diminish the herbaceous shoots? 

Kitty
neIN, Zone 5 
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