Dear David,
I am a cat ( and dog ) person myself & had the experience of needing a temporary accommodation after a house fire a few years back so I am speaking from personal experience as well as book learning about cat psychology. Dogs are pack animals and, for the most part, if their human leader is with them, they feel pretty okay about whatever place they may be staying. ( they are most likely to trash a place if left alone for hours)
Cats, on the other hand, are territorial creatures and it is very stressful to be put into a new and unfamiliar territory and they are not fans of car rides in the first place. An unhappy cat in a strange place might well do some editorial peeing/marking of territory. My cat didn't do that but she did have an upset stomach about the move and did a lot of spitting up & lost a significant bit of weight. Our dog was just fine. If you can find a pet sitter, your cats will probably be much happier and you will have many more options to rent. Your cats will miss you and might snub you at first when you return but isn't that better than miserable kitties? Also, if they get out of your rental, and they will be motivated to try, you might lose them forever. Your cats might be the absolute exception to all this but it's a risky experiment for all concerned, Sally