Jap,
I will chime in and state that the choice of a 4 AWG CEE would be compliant from the meter enclosure [it is on the supply side of the service which is compliant with 250.24(A)(1)] but some AHJ's like to cite 250.68(A) and say it is not accessible, but that applies to the connection from the GEC to the Electrode so that one is easier to fight.
You are given three (3) methods to handle buildings or structures with multiple disconnections means in separate enclosures in 250.64(D), you simply have to choose your poison from option (D)(1), (D)(2), or (D)(3). The option you have chosen with the meter layout is (D)(3). Now the POCO may not agree and have some issues with it which then leaves you option (D)(1) or (D)(2) to contend with.
As for the 1/0 CU you mention, would not be needed in any of the situations you display, in (D)(1) it speaks of general rules for installations like waterpipe, structural steel, however in your case you have a CEE which (D)(1) says the common GEC shall be sized with 250.66 (note it does not say Table 250.66), so if it was a waterpipe ground or structural steel ground then you would follow the directions in (D)(1). However, since it sends you to section 250.66 you will see that 250.66 says "except as permitted in 250.66(A) through (C).
Subpart (B) says that if this is the sole connection to the CEE then 4 AWG CU is all that is needed.
I do have a lot of people that say, no that (D)(1) says that "based on the sum of the circular mil area of the largest ungrounded conductor(s) of each set of conductors that supplies the disconnection means" is how you would size the common GEC, and thats simply not correct, a ground rod for example can only handle a specific amount of current as tested and how 250.66(A) was derived, what good would it be to install a 1/0CU to it when it can only handle what a 6 AWG can provide? Basically, those "instructions" in (D)(1) are telling you how to size it generally since section 250.66 does not provide those directions but clearly 250.66(A) through (C) are permitted.
Can you install 1/0CU to the CEE , yes, you can install 500 kcmil CU to the CEE if you want as long as you find a terminal device that will handle it but thats a choice above the minimum code standard.
Hope this was helpful.