I agree that the cassette teeth are well worn and not surprised that some skipping is starting w/ a new chain.

I've used the Rohloff tooth checker for quite a few years. It is less a go/no go gage and more a wear indicator type of tool. The "tell" is dependent on how its applied and used, one wants to keep all but that last link pressed onto the teeth while the lever is tugged. For larger sprockets (aprox 22T and bigger) this is harder to do (and IIRC the instructions mentions that this tool is for 21T and smaller). Unfortunately as is too often in a shop setting this tool has gone AWOL. We just ordered two of another brand's version and I expect much the same working limits and results. Soon I'll find out for real. Andy (who likes being able to use a tool to demonstrate what we see to customers).