Even when you use hay piles, the pile won’t ever completely disappear as they will forage through and pick out the bits they like. You can then fluff it up and top it up with fresh several times a day so they can come and forage through it again. The remainder of the pile can be thrown away once or twice a week (or any wet hay thrown away daily).
I personally find hay racks or anything small in which hay put in (ie hay racks, toilet rolls, tissue boxes) be restricting even if easily accessible (ie can reach up to them) - they’re fun and provide some enrichment but they don’t tend to eat it in the same way from those items as they do being able to get right into a big, loose pile of hay and freely forage through it.
If you want hay to be contained then large plastic under bed storage boxes with a door cut in or cardboard boxes (although they will obviously need replacing once they’re peed on) are great as the hay stays in one place but they can get right inside it.
Mine are entirely bedded on hay and even when they are laying around, their faces are always in hay and they’re always picking at it even if they aren’t physically moving.
They tend to be more active during early morning and evening, and while they only really sleep for short periods during the day, you would expect them to be out and foraging regularly.
What other kinds of enrichment do they have in their cage?
Have you tried different types of hay?
How often do you top up their hay?
Do you scatter feed veg and pellets or do you use bowls?