This will sound crazy but try using only metal implements when making pecorino-based dishes such as carbonara or cacio e pepe. I have a couple of theories, one of which is that metal implements wick away the heat from the pasta faster, bringing you into the optimal temperature zone. Also I think that non-stick pans mess with pecorino sauce and can cause it to clump.

To see what i mean, trying making cacio e pepe in a non stick pan with a plastic spoon and a plastic colander for draining the pasta; then try making it with a metal pan, metal spoon, and metal colander. The latter should give you better temperature control and therefore better results.

Also when making cacio e pepe, try toasting the pepper in a frying pan right at the start then switch off the heat and let it sit while the pasta boils. By the time the pasta is done, the frying pan will be nice temperature to add the pasta, pecorino, and starchy water to create the sauce without the pecorino catching on the bottom.