I am a bit late to the party , but has renting a walk-behind brush cutter been considered?
We happen to own one and it can cut brush up to 3'' tree saplings , does very well on all kinds of tough weeds and brush . That size of area could be done in an hour or two .
Of course I would go the goat route
we also have a couple goats
and yes they love poison ivy but do not let them kiss you after eating it
been there done that not a good thing