vagulus:
In short, can I, and how do I, assign other pins for SPI?
I think not, and much more to the point would be your explanation as to why you would want to do that.
The ICSP cluster is simply an alternative set of the same pins. It is common to both Uno and Mega, while pins 11,13 are not SPI on Mega. SS is not part of the ISP bus. Pin 10 is just a common and obvious choice.
Some devices have software SPI , but that doesn't mean you get to change Arduino's hardware SPI.