Removing a Cornelian Cherry Dogwood

Hi,

We're having to remove an established Cornelian Chetty tree in order to build a garden room above where it is. So far, we've removed most branches and are left with a 4-foot truck (about 1 foot diameter). The next thing is to remove that and most of the roots.

From reading about this type of tree, it has a dense root ball and the roots do not spread that far. However, the roots are prone to sprout suckers. I was planning to dig around the root ball and use the remaining truck as a lever to help remove it. But what I want to avoid is leaving root ends in the ground that will result in suckers coming up after a while.

What would you recommend? Would it be better to cut it to a short stump and use a root killer before trying to dig it up? Or would another method work better?

For more info, there are no other plants nearby and the tree is next to a neighbouring fence.

Thanks,
Steve