It seems to me that both the "Twin Earth" experiment and the question of "which physical process can be legitimately interpreted as a computational process" can be easily solved if you view them as questions of degree rather than binary:

1) Having an identical twin on another Earth is the same as being uncertain about where you are. If I am uncertain whether water is H2O or XYZ, then my idea of "water" refers to a probabilistic mixture of H2O and XYZ.

2) The degree to which a physical process represents a computational process depends on the simplicity of the program that prints out the latter given the former.