If research on that front yielded results, that would certainly be valuable.
But compare that task to the work that climate advocates have been doing for decades. Educating away people's political convictions has seen very limited success when it comes to convincing them that radical action on climate is needed. A similar effort on nuclear power might take decades more (which we don't have; as we know, there's a ticking clock).
The conservative-support argument is interesting, but IMO also flawed. Andrew Sullivan, influential conservative writer/intellectual, called for something like this when he proposed a 'nuclear Green New Deal.' In the United States, it's a non-starter. The politicians and voters who are interested in big, sweeping transformations of the economy are disproportionately concentrated on the political left. So is the most die-hard anti-nuclear opposition.
And this presents a coalition-building challenge. The American GOP is unwilling to take action on climate, and are heavily influenced by money from coal, oil, and gas interests. GOP politicians have, so far, refused to take even modest action, and appear to be comfortable making decisions on issues like climate or healthcare policy that are out of line with the public opinion polling, even with their own voter-base.
In the current American political landscape, bipartisan action, especially when it comes to a Green New Deal, or a 'nuclear new deal,' is currently nonviable. The last ten years of GOP opposition to the ACA, which was a small-c conservative proposal originally floated by the GOP (and tested by Mitt Romney), speaks to the lack of bipartisan options. So American action must come through the Democratic party, and leaning heavily on new nuclear power currently reduces the chance of that happening.
The international situation isn't much better. The conservative CDU/CSU is Germany has vowed to transition off nuclear power entirely. There's also the added problem that many countries are heavily dissuaded by the international community from acquiring and enriching nuclear material.
I agree with you and bdixon that emission reduction should be a serious priority for EA, and also that we shouldn't minimize its direct effects on human beings. The WHO estimates that between 2030 and 2050 deaths from climate change will reach 250,000 per year. Right now, its likely over 200,000 per year. These deaths don't come simply from heat stress, but also from diseases moving into higher latitudes, droughts, water stress, etc. My understanding is that this estimate does not include the impacts of war and conflict, which are also increasing as a result of climate change.
I disagree, however, that nuclear power presents a viable solution. I am in favor of nuclear power as a technocratic policy prescription, and I would be happy to see more of the world's power become nuclear. But it's not politically viable, and that's what matters.
Nuclear energy is unpopular. A 2011 Ipsos poll (admittedly conducted in the wake of Fukushima) found that only 38% of the population in 24 countries supported getting some power from nuclear. In the US, support for nuclear power is declining, and it no longer has majority support with the public, according to Gallup polls. These numbers can and do shift over time, but getting the public on board with nuclear is a long-term, challenging task. If you agree that massive emissions reductions in the next decade will save many lives and reduce our risk of triggering nasty feedback loops, like a collapse in land-ice, nuclear is not the way to go.
This dovetails with the larger question of tractability. In technological terms, climate change is a solvable problem. There are two reasons to think we might not solve it before triggering mass migration, economic collapse, world war, and nuclear/biological war. 1) The political system has consistently failed to take even modest action. 2) We are running out of time, and the solutions we will need to take only get more drastic the longer we wait.