I think this situation and many of the above comments are a perfect illustration of how the "vehicular" mind set can be inadequate (and even somewhat dangerous).

My goal would be to safely clear this intersection as quickly as I possibly could regardless of "the rules of the road" or "the feelings of motorists". How I would accomplish would and should vary:

If the speed differential were very high I might cross at an intersection/crosswalk (e.g. the exact opposite of biking like a car: pedestrian biking! ).

During very heavy traffic I might use the bike lane and try a quick dart across when there is a gap (driveways can be useful for this). In this situation I might even salmon up the bike lane on the other side for a bit.

If one were to take the lane I would recommend occupying the left side of the lane and doing their absolute effing best to not bike predictably. When placing yourself abruptly in a lane its very important to move around to increase your visibility AND discourage passing. Predictable cyclists are all too often invisible to inattentive motorists despite the presence of safety nanny prophylatics, such as, hiviz clothing or a dim tail light. Cyclists even have a specific term for this type of collision: Sorry Mate I Did Not See You. (SMIDSY)

Another high skill manoeuver mentioned above is to split the two lanes (esp when the lanes are wide or traffic is moving slowly). However, I think only riders who are a) very comfortable riding in close proximity to traffic and b) very confident in their urban bike handling skills should routinely attempt this manouever. My personal experience tells me that lane splitting can be the safest option in some contexts but for most others this would never feel like (or be) a safe manouever.