Some clarification of terms might be in order.
If the inside panel has the 1st disconnecting means then your "feeder cable" is a service and splicing of service conductors is covered by 230.46
Your service entrance disconnect has now changed location. A 4 wire feeder will now be required with isolated neutral at old SE location. GECs now need to originate at new disconnect.
Didn't you bid it high enough to put in new wires? The existing could be cut and reused between meter and new disconnect if of correct size, temp rating etc.
Does it say you can't? The NEC is permissive by omission.
My interpretation was that you were leaving the existing meter can and installing a disconnect under or near it. You could have used that existing wire, if all else was correct, to feed a new service disconnect.