I agree with your description of Penrose's Goedelian claims (the logician was Solomon Feferman), but I'm not sure why you say he'd be even more out of his depth in physics. Penrose is primarily a mathematical physicist, not a mathematican.
That said, his physics work seems to have been in general relativity, not quantum mechanics. Given what I know about how he messed up when he stepped out of his area in math, I find it more likely that he has made similar types of mistakes in quantum mechanics than that he has truly demonstrated that mainstream physics is wrong.
Except the twistor formalism he created (following ideas of no one else but Dirac) is important branch of research in quantum mathematical physics and string theory, not only classical gravity.
Just like Hawking or Freeman Dyson had, Penrose too earned his right to odd, and even braggart opinions on everything. Especially since opinions are by definition not meant to advance knowledge, or demonstrate results, but to provoke and inspire discussion.
In my opinion that paper is on the list of the 10 most important discoveries in science in the last century. See http://bentilly.blogspot.com/2009/09/what-makes-it-science.h... for the rest of that list.
Thank you for this most kind and substantial observation. In my defense, Hoyle used to joke of himself like that since concieving his steady-state cosmology where matter constantly flowed out of a "hole"; his autobiography "Home is Where Wind Blows" is also a good read.
In my opinion that paper is on the list of the 10 most important discoveries in science
Took cosmology course (with very distinguished cosmologist) and heard of that in passing. Since then forgotten, sorry (It was that important to me, maybe as a footnote to the αβγ mechanism. Of course this says more about my ignorance than importance of Hoyle's legacy).
So then, I view Hoyle as a crank out of my ignorance, you view Penrose as a crank out of your apparent ignorance. Further discussion would not be a rational argument.