Sounds like we may be getting confused over our recommendations. Allow me to re-state them as I understand:
For the cathodes: 8 x TIPC6B595 shift registers, daisy-chained (+64 suitable series resistors). 74HC595 not suitable for this due to overall chip current limits.
For the anodes: 1 x 74HC595 (also daisy-chained to the TIPC6B595s), driving suitable pnp transistors or p-channel fets. 74HC595 OK here as it won't need to sink/source much current - just enough to drive one transistor/fet at a time. It appears to me that 8 x TIP125 would be suitable (with 2K2 base resistors), but this needs confirming or a better suggestion.
Paul