Here's what I did. (I should emphasize that we were down to 2 rolls for a family of 5 and this was the only place I could find some and the only way they would sell it - I'm NOT hoarding).
Search for office supply companies. I literally googled "Office supply warehouse". These are places that will provide furniture, desks, office equipment, breakroom and RESTROOM supplies for businesses. They sell the large rolls of toilet paper that you find in office buildings, etc. You'll likely need to order a pack of 12 or more, but it will only be about $50-$70 bucks and it will arrive in 3-5 days. It won't fit your standard dispenser of course and it won't be the best quality, but it is softer than a paper towel and it's made to go down the toilet and it will last you as long as thing whole situation will last.