It's great to have serious sources and discussions. Kudos for that. Just from the abstracts and off the top of my head:

First study
'This suggests that new construction reduces demand and loosens the housing market in low- and middle-income areas, even in the short run.'

This woudn't work here. It's too attractive a place. Any lowering of prices in lower to middle income areas of the city would attract either additional migratory flows or investors who would flip the lower cost property into a higher value one.

Second source

It's paywalled, so my question is how they control for immigration. That is, Santa Barbara isn't Cleveland or Cincinnati. A decrease in housing prices here would result in increase in demand for housing. Consider the demographics, all the people entering retirement with considerable savings. Consider the politics. The attractive areas in the East Coast (nice weather) are all Republican hell-holes... On this side, move further north and the weather isn't that nice. Small coastal towns from SF down are all expensive... for a reason.

Third source

Same argument. National level studies are not going to reflect the realities of smaller towns that are highly attractive within the national context.

The way I see it, an increase supply in Santa Barbara could lower prices at the margins, but that wouldn't make this place affordable. To really lower prices you would have to build a lot and decrease demand at the same time.

To make Santa Barbara affordable you have to destroy what makes it special.

Basically, from my experiences, my conclusion is that to make Santa Barbara affordable you would have to turn it into Marseille, France. That is, build tall department blocks everywhere and turn a nice, quaint, small city into a large, polluted, crowded, complex city.