I haven't had any issues with this type of venting on any of the vintage rigs I've owned.
I don't think the screens in the floor let in any critters. I have had wasps built a nest in the roof vent, and end up inside.
A piece of regular aluminum window screen on the vent stack stopped that problem. Some would say this will decrease the airflow but I haven't had any cooling problems since installing it. I would hesitate to put a smaller mesh screen on the bottom as it may collect a coating of road mung which would definitely affect the draft.
If you're really ambitious you could fashion a sliding metal cover of some type for storage. I'd do something cheap like self-stick velcro and a old piece of plastic.