Oh well then definitely go with the dish ones! And you can make them with 1/4inch cloth for mice. In fact many people suggest 1/4 for mice cause they shred less food that way. It will just be twice as many squares around and tall, remember to measure for your tubs, don't just use my numbers. I just had lots of 1/2inch laying around. lol. oposite of you.
Just make sure that you make the rolls of mesh taller than your tub so that they will fit tight under the lids. You can always trim them down if they're way too tall. But you want the lid to pinch them down, that way the mice can't tip them over or climb in the top to steal food.