AES with shuffleBytes instead of shiftRows
AES ShiftRows operations ensures that each new column contains one byte from one of the 4 old columns. Thus it achieves Full diffusion in 2 rounds. 

You are right that there could have been other arrangement / shuffle of bytes to meet this criteria too. But if we analyze AES design, we will find that speed and memory requirement on all types of platforms were also given due attention in designing AES components. For example


MixColumn Matrix values are kept to minimum possible, like 01,02 and 03, which are fastest to implement as 01 is element itself, 02 is just left shift by One 03 is Exclusive OR of 02 and 01
Only one Sbox was used for substituting all state bytes
RCons in key schedule were kept minimum possible with simple in values.
The Shift Rows in 32 bit processor is just (i*8) left rotations of ith row where i=0,1,2,3. In case of 8bit processor, the first row elements remain unmoved and others are shifted based on index. 


so if you try to do random permutation or some fixes shuffle bytes, you will end up needing more resources/time on some or all platforms.

But if you dont plan to run you AES variation on all platforms, then you can introduce your own platform specific operation (offcourse security of which still needs to be vetted by experts)