Wow! I just slayed about 30 baby mexican fan palms yesterday with a hand saw. They pop up everywhere! Serious weeds here. They are really tough to dig out, once that tap root gets going. Easy to slay though. If the growth stem is severed, the tree will die. Not sure if it would't provide too much competition for the fig though. I'd go with the fencing, and will for sure once we get things in-ground!
Suzi