[X] See if there are other pieces of heavy tree-furniture that could be easily toppled over if you need them to. Could always use the environment to do your fights for you.
[X] Cut a part of the vine-rope you carry and use it as a tripwire. Unlikely to work, but if the zombie is really as retarded as it tries to make itself look...
[X] Try to hide and see what is it that tries to enter.