This is a radical departure from your actual question, but… Have you considered a Litter Robot? Yes, flies in the face of your question about cheaper solutions, but hear me out – long term, my LRs have saved me $$$ in cat litter and hours of labor/time.
I have 5 cats and feel your pain on how often they pee and how much wastage there is. (side note: I buy the 35lb Tidy Cats from Chewy).
My single LR cut my litter wastage more than half. Before the LR I had 2 regular boxes and went through 6-7 35lb pails a month. Now I have 3 boxes (2 LRs, 1 regular) and go through 3 pails/month. I think this is because the pee/feces is removed immediately (you can program it to run immediately after a cat uses it). This is also much more sanitary than regular litter boxes.
I liked the first LR so much, I bought a second LR a year later.