The criticism that there is no reliably reproducible demonstration of psi

How can you misunderstand something as simple as this: extraordinary claims require extraordinary evidence. 

That's an aphorism made popular by Carl Sagan but it's not a principle of the scientific method, as per the agreed upon definition linked in my previous post.
Just parroting the above adage doesn't make it true. Also the "extraordinary" qualifier is very arbitrary and based on your assumptions of what goest out of the "ordinary".

The usual example is that the claim "there's a red car in my yard" is more likely than the claim "a UFO landed in my yard" therefore the latter would require extraordinary evidence. In reality, if we had to apply the scientific method there wouldn't be any difference. If you think you can make your experiment less rigorous when testing for a "red car in my yard" then you're just making bad science.

Other than that every step of the scientific method wouldn't change an inch, regardless of wether you're looking for a red car, a UFO or the mighty spaghetti monster.

Also anyone with a shred of intellectual honesty would question the idea that ESP/PSI is an "extraordinary claim". ESP is tightly related to consciousness which in turn is the biggest mystery in the universe. It has no place in our standard model, it doesn't even have a place in the philosophy that drives most of our sciences, and top it all off
there isn't a decent theory out there that can explain what are the necessary and sufficient conditions for its existence.

To claim that ESP is an "extraordinary" phenomena we would need to at least have figured out what consciousness is, and be sure that that the two are at odds.

A hot stove will burn your fingers if touched? Or there's this mysterious stuff we know is there but which does not interact with ordinary matter or itself, but only interacts through gravity?

Come again?!
What has this to do with anything?