You're stuck between a utility rock and a NEC hard place
Normally, if your utility says to do something in a certain way, I'd agree with them and go along with the flow. However, your utility's requirements pose a significant problem here, namely, stray neutral current. You see, wiring up a service with metal conduit between meter and main panel and the grounding electrode conductor being extended through the meter base's lay-in lug to the main panel creates three possible paths for neutral current, since both the meter base and the main panel have the neutral bonded to their respective enclosures.
As a result, this multi-pathing of neutral current between the normal neutral, the metal conduit and enclosures, and the section of grounding electrode conductor running through that conduit creates what's arguably the "objectionable current" that NEC 250.6 is intended to be used to remediate. So, if I had any say in the matter and could ply the ears of your utility inspectors, I'd replace the metal nipple from meter to main panel with Schedule 80 PVC and also terminate the grounding electrode conductor at the meter base grounding lug, citing the "shall be permitted" language in NEC 250.6 with regards to objectionable currents both on cabinets (panel and socket enclosures) and the GEC itself.
Barring that, your only other option would be to find a meter main that your utility approves of and install that in place of the meter socket. This obviates the issues with what your utility specifies for a run between the meter base and the main panel, but it does not appear your utility provides any significant specifications for such beyond calling out a Milbank ringless socket with no bypass means as a recommended part.