I'm not sure I get what the people objecting to filtering on the left would do in that situation. It's a busy urban road, you are riding along near the left, other traffic is overtaking you. Then the cars stop, then they start, then they stop again, because that is how motor traffic behaves in urban areas. When the cars stop, you and they are still at pretty much the same distance from the kerb. There is still the same space in front of you. Are you to stop every time something next to you stops? That would take a long time to get anywhere; even longer than in a car, because you would spend the same time stopped but your peak speeds are lower.
Depends on what I'm riding (I don't like filtering up the nearside on recumbents, because I can't see over the cars to spot pedestrians and watch what the traffic is doing) and the size of the gap.
If the cars are effectively forming a separate lane of traffic, then a decent gap is maintained and I'll filter - at relatively low speed and being cautious of pedestrians, though as discussed above, probably not slow enough to mitigate the effects of such a dooring.
But mostly the cars are moving out (closer to oncoming traffic) to overtake you, and moving back in again afterwards. When they stop you tend to end up with a decent sized gap for a car length or two, then pot luck depending on what the drivers where doing when the traffic came to a stop (and indeed whether they move over to deliberately block filtering two-wheelers). So you have a choice of either stay put, or filter up until the gap narrows and stop. I'll only bother with the latter if it actually helps make a decent amount of progress - either tens of car lengths, or perhaps it allows me to reach a side road I want to turn into, cycle lane or ASL or whatever.
In stop-start traffic I'll usually take primary and wait in the queue. It's normally on the approach to a junction, so primary is desirable and there's little to be gained by filtering.
Filtering on the right isn't often feasible because you have to get there, and also because when the cars start moving again, they will be undertaking you, leaving you as the slow vehicle between two opposing lanes.
Indeed. And often tempts you into conflict with oncoming traffic.