If you use the open tench method, you could create biochar right where you fell the honeysuckle.
Since the trench will already be there, you could add
more un-charred
wood, and cap it with soil left from digging the trench.
Leafy branches in particular might make for good
hugel materials.
What should be planted in such a hugel?
Is there any plant that would do well in competition with the honeysuckle?
Running bamboo could be worse than the honeysuckle.
Jerusalem artichokes are at least edible, if difficult to control
Black berries are a natural fit.
Peas are aleopathic, and nitrogen fixing.