I just realized actually one very likely reason you would see a significant increase like this. I imagine that the GoogleBot and Pagespeed servers are on the same network, or at least regionally close enough to make a big difference.
Cloudflare is not going to be on the same network as Google for any of their servers as they host their own gear around the world. If you want to see the real speed decrease from switching it should be a set of tests between Cloudflare and Pagespeed from outside both of their respective networks (and a couple locations if possible). That would give you closer to real numbers... or the google services are on totally different networks and what you saw was real-world, which I couldn't answer.
Cloudflare is not going to be on the same network as Google for any of their servers as they host their own gear around the world. If you want to see the real speed decrease from switching it should be a set of tests between Cloudflare and Pagespeed from outside both of their respective networks (and a couple locations if possible). That would give you closer to real numbers... or the google services are on totally different networks and what you saw was real-world, which I couldn't answer.