There is nothing wrong with sitting on the hay and it shouldn’t be considered wasted. Hay, while it is their main food source, is much more than just their food- it’s fun and enrichment also. They enjoy being amongst it, foraging through it etc.
I don’t use any way of containing their hay - I simply throw it in a pile on the cage floor and they immediately dive into it, forage through, run and play in it. They eat so much more being able to just be amongst it and eat where they lay.
If you don’t want to just put it on the cage floor (if yore using fleece it sticks. Mine are on disposable bedding so it’s not an issue), then I’d personally encourage you to just continue using the litter trays. Empty them daily and top up with fresh hay