Though I think "imminent mortality" is not the only thing at the foundation of age-driven conservatism. I think there is also tendency to follow paths of least resistance (energy conservatism): learning/discovering new ways of doing things comes with more friction (if one does not enjoy the learning/wandering process).
EDIT: I just realized that the two points are really intertwined. Time conservatism is closely related to energy conservatism and cannot be regarded in isolation. (forgive the awkward terms)
> ...if one does not enjoy the learning/wandering process...
Or, if one does not perceive that the investment has time to pay off.
The result you mention seems intuitively correct, and meshes with my own experience. The career changes that I'll consider in my 40s are definitely not the same ones I'd have considered in my 20s. There's no time!
It's not a disinclination to starting over that fuels (social) conservatism, but rather a yearning for an older, simpler, "more virtuous" time (one often that never actually existed, except in the imagination).
This is how you wind up with old people wearing clothes that were fashionable in their youth, still behaving in "old fashioned" ways, still consuming media from bygone eras, etc. Not that such behaviors and tastes necessarily make you a conservative, nor is this restricted to just old people. Some young people also yearn for the past, and enjoy affecting styles of dress and consuming media from bygone eras. But the cause of such sentiments is shared with conservatives: that is, it's a rejection of modernity and a yearning for a mythical past.
People who are "living in the past", as it were, or wanting to re-create the past in the present aren't interested in reinventing themselves or embracing the present or the future. If anything, living for longer is likely to exacerbate this. The feeling of nostalgia and yearning for an older time is likely to get worse, and the inability to cope with the modernity is only likely to increase (barring breakthroughs in psychology, sociology, neurology, or psychopharmacology that might make such coping with and accepting of the chaotic and ever-accelerating present/future easier).
As with a lot of tropes, we're having trouble nailing down terms, too. As you allude, we've at least meant a few different things by "conservative;" 1) social conservatism, 2) technological nostalgia, and 3) scientific conservatism. This seems to be one of those memes (I use the word deliberately as a "persistent mental structure or coding," separate from the term "idea.") that survives by coding multiple actual ideas. Not that you're doing the following, but reciters of the meme can always switch between ideas/fields when the current case becomes problematic. Societies don't become conservative? Well, what about Kuhn/Planck and scientific conservatism? Oh, scientists do actually adopt new theories late in their careers? What about people who restore classic cars? People buy new cars late in life? Well, societies become more socially conservative as the population ages. And so on.
One final point that, again, you're not doing right now, but I find ironic and amusing. Critics of life extension will oft lament that "mortality makes us human," and that we'll become inhuman monsters if we routinely live to be 1000. Then, in the next breath, they'll then insist that we'll behave exactly as if we died at 80 when it comes to things like conservatism, or reproduction, or career choices. But that's just the amusing part; the ironic part is that they'll do this at just about any age!
> Nearly a third of Boomers (31%) and 36% of Silents described themselves as conservative Republicans or Republican leaners, which also is higher than in the past.
http://www.pewresearch.org/fact-tank/2017/03/20/a-wider-part...
Well, the main factor I'd say is that being older involves having accumulated a lot "functional" opinions and solutions to problems. That is, a lot of approaches that may not be absolutely optimal but work (and which would require a lot of time to work out alternatives to - in the fashion it takes a lot of time to train a neural network). So basically, it is extremely difficult for those who have a fully functional coping strategy to go back to "not knowing anything" and relearn.
I mean, while most people are more flexible at twenty than at fifty, most people are more flexible at ten than at twenty and it would be hard to revisit the "personality choices" that happened at ten when you are twenty even when mortality is a ways a way.
There was also a recent study suggesting a link between successful efforts to reduce birth rates in China and their higher political stability compared to neighboring countries, because the young bring instability while the old like the status quo.
Also, I'd really like to hear this "tendency of society to become very conservative" fleshed out. I think you meant "as average age goes up," but I'm not sure why "society" gets brought into it. Aren't we pointing to a tendency of individuals to become more conservative as they age?