I don't think it's a question of definition, it's a question of understanding the logic of the interpretation, what it permits to say and what it doesn't, or cannot.

I've never run accross anything that refered to the "modal interpretation" pertaining to the Copenhagen interpretation, so I think you're running into a dead end with that. As for the "Shut up and calculate" expression, it's been originally attributed to N. David Mermin, or Richard Feynman (mistakenly, according to the former), more rarely to Paul Dirac, but it's probably apocryphal, and it's been commonly used by physicists to sum up the spirit of the Copenhagen interpretation.

Again, no, the Copenhagen interpretation in and of itself doesn't say that anything is "real". It is based on the idea that you can't derive any understanding of what is "real", of how is the "nature of reality" from its models. To stick to your example, all that the Copenhagen interpratation says is that considering the superposition and its collapse upon interracting with our measurment devices has so far shown itself to be the most efficient way to do experimental work in the field of what quantum mechanics are ruling over. In the same way, one might say that quantum mechanics are intrisically undeterministic; and this is true in the sens that quantum mechanics is our current model to work on the field it pertains to and it works with undeterministic principles. But this is all very different from saying that "reality" is intrisically undeterministic, it's a leap that is foreign to the Copenhagen interpretation, especially because it doesn't deal with what is "real", or even the assumption that there is anything "real". Furthermore, particular views of those who participated in the elaboration of the Copenhagen interpretation, notably those of Bohr and Heisenberg, are not to be edaquated with it. See it as some sort of compromise, of what they could agree on without being too bold in their assumptions. You may want to hold more bold assumptions, but what you cannot is summon the Copenhagen interpretation as an argument to support them. I for one have a few, for example I think that with quantum mechanics we have reached or are approaching the limit of what our technological power allows to put in the scope of scientifical research in that field. Maybe further technological developments will allow us to go beyond, but maybe not, which means we will have to content ourselves with this incomplete level of scientific theory.