How do I fill a recurring sinkhole in the rainforest of Hawai'i?
Foam sounds like a bad idea to me for a sinkhole. I've seen them cover old wells with large quantities of foam followed by earth, but your situation is a never ending geological process caused by water flow. Have you read this about the Guatemala sink hole? The article suggests the right way would be to layer rocks. Very large at the bottom and smaller as you go up so that the water can flow through that area but doesn't take the soil with it causing another sink hole. I'd go that route if it was me.