Foliar spraying should be done starting in the late fall, when the native plants are dormant. In the spring before the sap is running go with basal bark or cut stump application. Those work in the fall as well. Thing to remember is that their is more than likely a huge seed bed there, so this will be a multi year project. Personally I am not a fan of foliar spraying anything that is over 2-3 feet tall, unless I am equipment that has a cab. I have seen really large patches cut off with a Forestry Mower (Fecon), let it re-grow till about a foot tall and foliar spray it in the fall.
Burning would probably be the most cost effective, if you can find someone to do it and get a fire to carry through it. If you have enough fuel to carry a fire you would want a very hot and slow fire to make sure you cook it. You will have to re-burn or spray the new plants that come up out of the seed bed. If you open the canopy up, you will most defiantly need to control it, it will sit in the shade getting by and then really explode when it gets sunlight.
Hopefully you can get the neighbors on board also. You can clean it out just to have it come back from a bird that is feeding on the neighbors property and crapping on yours.