Can you keep the 'little lime' at 3" by cutting it to the ground in spring? Has anyone else done this?
Assuming you mean three feet, and you don't mean "to the ground" but instead merely "way back," sure.
Paniculatas are very forgiving.
I wouldn't do it the first year or so- I think I would wait and see how it does in your conditions before assuming it will be too huge. If conditions are lean it might stay smaller and if conditions are rich then even a severe pruning won't stop it from growing.
If your space limitations are three feet max no matter what and anything one inch over is a no go I might look for something else- they're too gorgeous left alone.