Hi Wes,
Your analysis of the graphic you posted does not jive with the graphic. In fact, the the AO was extremely negative for most of December and January. It didn't return to neutral until mid January, not the first of the year.
The AO is essentially a measure of the near-sea-level (1000mb) pressure in the arctic (poleward of 20N). When the AO is positive, the pressure in the arctic is low and when the AO is negative, the pressure is high. When the arctic pressure is low (AO+), this results in a stronger gradient between the pole and the mid-latitudes, resulting in a stronger, more zonally oriented polar jet, which from a thermal wind argument tends to lock in the cold air across the arctic. When the arctic pressure is high (AO-), the gradient between the pole and the mid-latitudes is less, resulting in a jet stream that is apt to meandering/buckling and thus cold air intrusions into the mid-latitudes.
With its relation to severe convective weather, it's a lot like the Pacific-North American Pattern (PNA). A PNA+ scenario is one where there is a west-coast ridge and and eastern tough. A PNA- scenario is one where there is a west coast trough, and an east coast ridge. Based on that, one might conclude that from a chasing stand point we would want a PNA-, right? Not exactly. We need to have a strong temperature gradient somewhere near the plains in order to have a strong mid- and upper-level jet, which is needed for severe convective weather. If we examine the PNA impacts on severe weather completely in isolation (meaning this is a theoretical argument), it is best achieved when the PNA is in the process of transitioning from one phase to the other. In other words, the really big outbreaks (severe convective or severe winter weather) tend to happen when the PNA is transitioning from PNA- to PNA+. In this scenario you have a west coast trough that is ejecting east into the plains, and being replaced by a west coast ridge. The west coast ridge tends to dislodge cold air from western Canada southward into the US, giving you a classic severe weather setup of cold air north and west, warm air south and east, and a strong, dynamic system in the gradient.
I mention the PNA scenario to tell you that if we examine the AO (again in isolation) neither the negative phase or the positive phase are extremely great for severe weather. Your best bet is when the AO is in the process of rapidly transitioning from one phase to the other. (As with the PNA, all things equal, the faster the transition, the stronger the gradients.) I'd tend to prefer a AO+ to AO- transition, since the AO- would have led to arctic air intrusions somewhere into the middle-latitudes, probably shunting the rich moisture equatorward. Not to mention that as the transition from AO- to AO+ takes place the polar jet would be lifting north. In the reverse scenario (transition from AO+ to AO-) the mid-latitudes would be relatively warm (and hopefully moist) so that when the arctic air surges south, there would be the possibility of severe weather along the boundary between the two airmasses. As with most things in meteorology, the really "fun" stuff occurs in the gradients...not the maximums (minimums).
Tying this back into the original question at hand, La Nina (or more precisely, ENSO) is only one source of influence on the overall large scale pattern. In this post I've identified two others that can have just as strong (or stronger) influence on the hemispheric flow -- and there are many others (QBO, NAO, MJO, etc). Meteorologists and Climatologists are just beginning to understand these teleconnections between the state of these large scale oscillations and the observed weather patterns. Most, if not all, of our understanding of ENSO comes from observations post 1950 (and, really, post 1970). Since the 1970s the AO has favored a more positive state, meaning that most of our understanding of ENSO's impacts are based on a singular phase of the AO -- AO+. Lately the AO has favored the negative phase, which means we're still learning what the appreciable impacts are when combined with ENSO states.