This is an interesting and somewhat counterintuitive phenomenon but we’ve seen it multiple times in recent years. The central and northern US seem particularly vulnerable to these arctic outbreaks, but so far it’s typically coincided with warm, dry weather in California—this year seems to fit the mold as well. But is this just coincidence or is it always going work that way?
This has big impacts on my work as an arborist—we’re trying to shift our palette of trees towards more southerly species to prepare for future heat. But if we occasionally experience exceptional cold, this can hamper those efforts as it can be deadly to more southern species. So far California has not seen this particular pattern but it only takes once for serious damage to occur.
I know this doesn't help with your project, but here's how I've managed the "intuition" part. Note that this is just the mental model I have, not actual science.
The jet stream (also known as the polar vortex when it dumps cold air southward) is powered by the temperature difference between the arctic and the subarctic. The arctic is warming faster than the subarctic, so the temperature difference is being reduced. That reduces the power of the jet stream.
The jet stream is like a wall that separates the arctic from the subarctic. As it gets weaker, arctic air "breaches the wall" or maybe the "wall" just relaxes and moves south.
Even though the arctic is rapidly warming, it's still damned cold, so it causes all kinds of problems when it escapes.
It could be just pattern seeking, but I feel that we in southern Saskatchewan are getting yo-yo weather as a result of greater fluctuations in the jet stream. We're just coming to the end (I hope!) of a dangerous cold snap. The week before it was near freezing (shirt sleeve weather around here at this time of year) and the forecast for next week is more of the same.
here is an explanation video with animations at around the 2:30 and 5:00 min mark.
The fast wind was moving more or less straight. Now that it slows down, it gets a wavy pattern, that also moves slower. As a result we get more stable cold zones and more stable heat zones. As these move slower over the planet, it results in longer cold and heat waves, with adverse weather. So the boundary doesn't get "breached" in one direction, but rather it relaxes in both directions, getting the yo-yo weather you describe.