Just curious what would prohibit one from doing both parallel current paths?
Your question could be interpreted a couple different ways depending on whether you mean to refer to different paths to earth as 'parallel' or if you are just referring to parallel paths to the same GES.
For the former interpretation, all electrodes in the system must be connected together, you cannot have separate paths to earth. 250.50. Note the OP's diagram seems to show individual GECs to separate-not-bonded-together electrodes, which would violate that section. Those individual GECs are only allowed if they all go to the same GES.
As far as parallel paths to the bonded-together GES, I think objectionable current, 250.6, would prohibit you from using both the methods in 250.64(D)(2)
and (3), and this corroborated by the fact that 250.64(D) starts out by saying that the connections "shall be made in accordance with 250.64(D)(1), 250.64(D)(2),
or 250.64(D)(3)." (Emphasis added.) Indeed, I would say that 250.6 would prohibit what is described in 250.64(D)(1) and 250.64(D)(2) if those same sections did not explicitly describe those methods as being permitted.