Darn. No gloves or lotion. There went my ideas.
When I used to do that same thing (washing hands every 5 minutes all day) sometimes I would have to resort to either hydrocortisone lotion (at most twice a day for a couple days) or a liberal application of a good lotion (Neutragena's Norwegian Formula) and then into a pair of plastic gloves for the night.
Outside of that, maybe a moisturizing hand soap. Are you using an alcohol based hand sanitizer after washing? Those can dry skin out like crazy, and with proper hand washing technique they aren't necessary.