More specifically, it seems that your c must include information about how to interpret the X bits. Right? So it seems slightly wrong to say "R is the largest number that can be specified in X bits of information" as long as c stays fixed. c might grow as the specification scheme changes.

Alternatively, you might just be wrong in thinking that 30 bits are enough to specify 3^^^^3. If c indicates that the number of additional universes is specified by a standard binary-encoded number, 30 bits only gets you about a billion.