I'm so happy for you, Toni. That's a strikingly unattractive tree and it absolutely dominates your garden. You're going to love having it gone!
I had a Liquidambar removed from in front of my house about 15 years ago (after the blasted thing actually lifted a corner of the house) and I did pay the extra thousand to have them grind the stump. In spite of that, I was killing suckers for the next 4 or 5 years. Eventually, though, even they stop coming up.