I understand you don't want to trespass and ask permission but its not like you will conduct work or make trails and what not its a momentarily trespass to make a situation safe for you, anyone would understand plus if one property is lease and the other one is a big corporation I wouldn't even bother to ask personally dealing with a corporation that tree has time to rot before you get hold of them, but that's me you do you... the risk with you plan will be to guarantee the top of tree doesn't bounce or spring back because of the branch's. It might simply not want to flip that way, it may damage your fence by doing it the way you are proposing but it also could work but luck you need to be on your side, if it happen it also might not be the end of the world ether but I figure you should consider that risk.