Here, change the perspective a little bit, yet keep the question the same.
Run the #4 from the main bonding jumper to the first 5 feet of the metal cold water pipe.
In my area, the water meter is inside the dwelling, in a pit, or exposed in the basement. There are two valves, the street side shutoff and the house side shutoff.
On the way to the first 5 feet of water pipe inside the dwelling, run the #4 bare stranded copper through a first water pipe clamp that is on the house side of the house water shutoff valve more than 5 feet from the water pipe entrance. Continue the #4 copper, unspliced, to a second ground clamp on the street side of the street valve.
I see the #4 as the GEC for its entire length. The first ground clamp bonds the interior metal water pipe (more than 5 feet) to the GEC.
Now, one might argue that the #4 between the first water clamp and the main bonding jumper in the service disconnect is only a bonding jumper and that one must run first to the street side of the water meter (the first 5 feet) and then back around the meter to the house side. I think the #4 between the MBJ and the first clamp is simultaneously both a GEC and bonding jumper, just like the OP's #4 between the MBJ and the distribution panel is simultaneously a GEC and an oversized EGC.
