Thanks for the feedback, PPs. (OP here.)
It's a small 12', but who knows what the root ball looks like.
I'm experienced gardener, but this plant has just been on my list since I bought my house. It's not the variety that can be pruned and bloom out in a nice shape; instead, this variety sends up volunteers all over this garden bed, including alongside the trunk.
All to say... if I hack it down with an axe, I don't know if that will even end the relentless volunteers.
You've both given me something to think about, though. Guess my big plans for digging it up myself may not work.