Your box predates the UL requirements for a feature known as Circuit Total Limitation (CTL). This feature restricts where double-stuff/tandem breakers can be installed in the panel to prevent it from exceeding its designed circuit capacity, which was restricted to a maximum of 42 circuits by the NEC (i.e. nobody could make a panelboard for more than 42 circuits). However, the 2008 NEC lifted the 42 circuit restriction on panelboards.
Practically speaking, I would go ahead and install the new double-stuff/tandem breaker provided that there is sufficient remaining wiring space in the panelboard gutters to accommodate the extra wire. You'll need a QO2020 (not a QOT2020, which won't fit) breaker for this.
(NB: All quotes here are from the 2014 NEC, but I know of no significant changes to these passages between 2014 and 2017.)
Methods 1 and 3 are fine...
For a 15A MWBC, both wiring method 1 and wiring method 3 will work and are Code-compliant as described, insofar as the receptacle wiring goes.
but Method 2 isnt...
Method 2, however, violates NEC 300.13(B) as described:
(B) Device Removal. In multi wire branch circuits, the
continuity of a grounded conductor shall not depend on
device connections such as lampholders, receptacles, and
so forth, where the removal of such devices would interrupt
the continuity.
as removing the first receptacle of the circuit leaves the second receptacle sans neutral. Fortunately, this mistake won't fry any equipment, but that's only because the second receptacle only gets the second leg's hot.
And all three of these need handle tying to be compliant
In any case, identified handle ties need to be used in order to provide the "common disconnecting means" required by 210.4(B):
(B) Disconnecting Means. Each multiwire branch circuit
shall be provided with a means that will simultaneously
disconnect all ungrounded conductors at the point where
the branch circuit originates.
Informational Note: See 240.15(B) for information on the
use of single-pole circuit breakers as the disconnecting means.
and 240.15(B) (specifically, 240.15(B)(1)):
(B) Circuit Breaker as Overcurrent Device. Circuit
breakers shall open all ungrounded conductors of the circuit
both manually and automatically unless otherwise permitted in 240.15(B)(1), (B)(2), (B)(3), and (B)(4).
(1) Multiwire Branch Circuits. Individual single-pole circuit breakers, with identified handle ties, shall be permitted
as the protection for each ungrounded conductor of multi-wire branch circuits that serve only single-phase line-to-neutral loads.
Best Answer
This is OK, as the manufacturer has a specific part for this job
Handle-tying the two inner half-breakers in a pair of (modern style) QO tandem breakers is legal, no different than handle-tying two full-size breakers save for a change in part number: instead of a QO1HT (the normal QO handle tie), you need a QOTHT instead (image from Square-D's product page):