The sickle bar I have for my Goldoni is very efficient in its use of power. It will cut through anything that fits between its teeth, and its narrow vertical profile will pass under 14" boulders that were hidden by the foliage when I started. It is efficient because it only cuts the stem once, leaving the plant behind to obnoxiously annoy the operator as mentioned by bcp above. The tops will have to be gathered and moved, pricking and scratching all the time.
I also have a Goldoni rotary deck. It was intended as a lawnmower, but the 22" blade is about 3/8" thick. It will chew up anything it can push down; puting 10 hp into a 2' swath should do that. This mower would be my choice for tackling your problem, although the "clutch" is problematic on unseen stumps, etc.
Goldoni is incomparable with BCS (different spline patterns). If you are haunting Craig's List you may find something reasonably cheap. But the notion that you will need it only once to control those noxious plants is delusional. Look at Earth Tools's website to get ideas on brush cutters and flail mowers for your BCS. If they are too dear, an old beater rotary lawnmower may work albeit very slowly.