You already have the answer - select the correct mulch. With the right mulch the leaves will stay cleaner and require less washing.
We cut our lettuce and do three rinses in a large basin (size of a dishpan), the used water is returned to the garden. Then into the kitchen for one final rinse. Salad spinner** removes the excess water, then pop them onto a flour sack dish towel and chill in the fridge.
Talk to the shelter and ask for one volunteer to come to your house and pick up the lettuce before you wash it. Let the shelter volunteers wash the lettuce.
**Note: I don't actually own a salad spinner; I hold the 4 ends of the dish towel and spin it over my head like a cowboy at a rodeo - my neighbors think I am insane but the dragonflies enjoy taking a shower when I do this.
