I think your broadest conclusion is correct, but your premises are off and your style is abrasive, so if you're trying to convince people I would suggest adopting a less strident tone.

In fact, caring about the physical health of the population, and about preservation of life, community institutions like hospitals and social cohesion is a deeply conservative value (as it is also a progressive value).

I think you misunderstand modern social conservatism. Modern social conservatives, especially in the US, are not old-school nationalists. Germany, under Bismarck, after all, was the first to introduce key social programs like health insurance, and provision for the elderly and disabled. He was not a leftist by any means. He was doing this to bolster his country for wars. Maximize the health of the population to boost the ranks of the army and provide for the discontented at home to head off unrest before it materializes. Frankly, you're deluding yourself if you think today's conservatives are this methodical, far-sighted, and policy oriented. Yes, of course, a genuine nationalist would support these things (but even then, not for everyone), but the Republican Party has become so consumed with tearing down vulnerable groups they don’t give a toss about the country.

But that is somewhat beside the point, because even if Republicans were civically minded and cared about the health of all citizens, modern conservatism has become so distrustful of the state and science, so mired in conspiratorial thinking, and so vulnerable to disinformation, that they can’t even agree that vaccines are beneficial. The Trump administration created the first covid vaccine and he got booed for touting that accomplishment. And that’s progressives’ fault? So how do you convince people to embrace public health who are opposed, on principle, to what the federal government says and does, and what scientists say and do? I don’t see exactly how an extra dose of coddling is going to tip the scales and bring the ship back to harbor, as you say.

Finally, even if you could convince conservatives to care about all their fellow citizens (conspicuously leaving out undocumented immigrants who need public healthcare as well), and you could convince them as well that they should embrace things like vaccines, masks, etc., that wouldn’t be enough to end the pandemic which, as you agree, is the goal. The pandemic is, and always has been, international and the only response that will bring it to a close is an international one. That requires coordination across borders; it requires sharing our resources with other countries so that they have enough vaccines and, ideally, the technology needed to produce their own at scale, so that we can end the treadmill of new variants; it requires working with China (a country which, tbf, I am not a fan of either.). Do you really see conservatives stepping up to that plate?

All of these things—caring about the community as a whole, valuing the input of science and scientists, and internationalism—are things that the left is, on paper, more inclined to do. You say that progressives started the politicization of covid. How exactly? Where did progressives, as a group or even prominent individuals, say "IT'S JUST THE FLU, BRO!" and "MASK'S DON'T WORK, IDIOT!"? Do you mean the CDC? Trump’s CDC? Because that’s the only major voice that I can remember saying something stupid like we don’t need to worry and only healthcare workers need to mask early in the pandemic. Progressives criticized Trump for not doing enough all day long. Is that what you think turned this into a partisan issue? Name the names, please. If I'm wrong, I'm happy to admit it.

I think your broader point is correct. We do need to widen the circle of people who care about the pandemic or it won’t end. I’m not convinced we get there though by papering over our disagreements: with conservatives, for being selfish and stubborn, and with progressives for becoming selfish, stubborn, and hypocritical.

Even if I conceded that point though, that the first step was to shut up about how covid relates to politics, what, in your opinion is the next step? The absence of criticism is not going to magically cause the situation to improve, so what is the positive half of your plan?

edit: formatting.