Can I convert my oven to a four prong?
You'll need to use a 10AWG ground pigtail here

For a flush mounted box, NEC 250.146 and in particular 250.146(B) form the controlling Code on how to ground the device(s) inside:


  250.146 Connecting Receptacle Grounding Terminal to Box.
  An equipment bonding jumper shall be used to connect the
  grounding terminal of a grounding-type receptacle to a grounded box unless grounded as in 250.146(A) through (D). The
  equipment bonding jumper shall be sized in accordance with
  Table 250.122 based on the rating of the overcurrent device
  protecting the circuit conductors.


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  (B) Contact Devices or Yokes. Contact devices or yokes
  designed and listed as self-grounding shall be permitted in
  conjunction with the supporting screws to establish equipment
  bonding between the device yoke and flush-type boxes.


Since your receptacle does not have a self-grounding clip on the mounting yoke (I know of no receptacles >20A that do, even), you will need to use a bare or green 10AWG copper wire from the receptacle ground terminal to a 10-32 screw in the designated grounding hole on the back of the box.  This will ground the yoke, faceplate, and receptacle grounding terminal, without relying on the receptacle mounting screws as a grounding path.

As to that sheathing...

Since this is an existing run of cable, and the straight NEC does not limit the ampacity for which AC sheathing can be used as a ground path, I would use this sheathing as a ground, considering the obvious alternative (NEMA 10) is quite a bit worse here.  There is also the option of running a 10AWG bare copper wire back to the panel or grounding electrode conductor/system by any route possible to serve as a retrofit ground conductor as per NEC 250.130(C).

(The subpoints to NEC 250.118(8) you mention are Chicago-area specific amendments to the NEC.)