Thank you for your response Porter57, if you like them so much you can have them :-D Here in Florida, Elephant Ears are just another
weed. Some people like them, but I personally think they are a waste of perfectly good planting space. Also, if I don't cut them back often there multiply quicker then rabbits. The other big problem with them here is the fact they are a haven for snakes, and we're going to be adding a new puppy to the family shortly.
In response to your comments...
Well I am not opposed to blanketing the area with something, everything there that is green can be killed as it is only Elephant Ears and a few
weeds that I haven't bothered to take out.
I am trying to avoid having to dig it all up as like you said it would be a big chore. Although if the only option is to spend a Saturday out there digging them up then that is what I will do.
If someone has a chemical method to recommend I would appreciate it. However I am going to be using this area for an herb garden when all is said and done (basically I don't want anything that will have lasting effects on the ground).