We booked 2 weeks in a short term rental and ended up in another short term as could not get anywhere. Sometimes you turn up for an open and there may be 50 people looking at the house. A few we just turned round and left as there was so many people looking. You can always write a letter to the owner to put with the appilcation stating that you love gardening so will look after the garden, basically sucking up to them, thats what we were advised to do. Alternatively you could do what I did and talk to the agent, tell them that you are in short term and soon have to be out, start crying and act really pathetic and you get the house!!!!!!! Obviously I didn't plan to do that but it worked lol.
Just take as much evidence with you as others have suggested, good luck