If they are permanently in the house, I would use up the straw and then just use hay for both bedding and eating - it makes maintenance and shopping easier. Straw has no nutritional value for rabbits - although it is a really good bedding for outdoor bunnies in winter. They really need to eat LOTS of hay (or grass), so the more they have access to, the more likely they are to become good hay eaters. Just take out the soiled bits daily and keep filling up with fresh stuff as you are doing.
Bigger 'litter trays' may also make things easier - the underbed storage boxes are used by lots of people on here. You have enough space for them, and it may encourage the bunnies to spend more time snuggled up eating hay and using it as their toilet at the same time.