You said the unwanted growth is large. Would you be able to peel back a large portion of the bark from them? That would probably be the best way since you want to keep the fruit trees. The more bark you can remove, the better.
It would still take some time for the excess growth to die out. I'm not sure whether it's possible to find out how long it would take with some research, but knowing the two types of trees that are the intruders will help.
Even if the previous homeowners took care of their fruit bush and tree, they probably wouldn't have thought to look inside of each to monitor unwanted growth.