That is so frustrating and heart breaking! Thank you for advocating for the cats <3 Do you have colleagues in the shelter who are on the same page as you? Sometimes change can be made when there are many voices supporting it.
Our shelter uses pine pellet litter primarily, with the full understanding that it's not ideal for the cats. If a cat doesn't use the litterbox for a day or so when they first come in, or if they use their bedding, we switch them to clay and recheck the next day. If we have a cat surrendered for house soiling we place them in a room with 3 litterbox options (clay open, clay covered, pine pellets open) and monitor while awaiting urinalysis. Simply having a non-scented, fine-grain, clay litter in a large, open litterbox solves our non-medical house soiling cases most of the time.
All house soiling cats should have a thorough medical exam. Perhaps that's an angle you could use? Euthanizing cats for house soiling without determining if there is a medical condition is poor practice. If there is pushback against the cost of medical care for all the cats who are house soiling, that's when you bring up that there would be fewer cases of house soiling cats needing medical exams if the cats received a more preferred litter.
Then have a plan in place for a proposed change. For example; All cats start with the shredded newspaper litter (starting at the point where upper management wants to be). If a cat does not urinate or defecate for 24 hours, they should be offered an alternative litter (this is for the cat's health and wellbeing). If a cat soils their bedding X number of days, they can be offered an alternative litter (this is to rule out house soiling due to litter substrate preference and can reduce the number of cats being flagged for medical exams). If a cat continues to house soil, they are flagged for a vet exam to rule in/out medical conditions.
Have a clear outline of exactly what you would like to change; who would be involved and what resources do you need, how the change will affect the cats wellbeing (and the wellbeing of the volunteers, staff, and public who interact with the cats), and ask to test this as a pilot project for 2-3 months so you can gather data about how effective the changes are. Also include what data you would like to track; number of cats in the shelter, number of cats not using their litterbox, number of cats euthanized for house soiling, how much litter is getting used (and what types), and anything else you think is important for the decision makers to know. Get those numbers for the last couple months so you have a baseline to compare to.
And as Kate said in their comment; poor sanitation is a massive welfare and cost concern. Use public opinion in your favour for creating positive change in your org.
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Alicia Naundorf
RVT
Edmonton Humane Society
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