I've looked because it's an interesting modesty argument: if older people reliably are more conservative and have more information, on what grounds do you not immediately become conservative yourself? (And variations thereof.)

Has anyone looked systematically at what projected older versions of themselves would think, based on what relevant groups of existing older folks think?...My dim recollection of studies is that on the whole as people age they tend to be less idealistic, more resigned to society the way it is rather than how it might be, and more constrained by realities of politics and economics (for starters).

There's an obvious confound: the aging itself induces negative changes. 'resigned' can just be a synonym for 'tired' or 'lacking in energy'. Aging also introduces many other negatives - your intelligence takes massive hits: http://www.gwern.net/DNB%20FAQ#aging I'm 24, so compared to my 60 year old, I'm something like 1.5-2 standard deviations smarter (disclaimers: average, z-scores over general population, I hope to do better, etc.).

My IQ is somewhere in the 130s, and a standard deviation is usually something like 12-15 points, so taking advice from my future self would be like taking advice from a normal 100 IQ person now! I don't pay terribly much attention to what such people say... I'd still pay a lot of attention to any message from the future because my future dim elderly self has all the fruits of my higher IQ periods to draw on, but this observation is enough to largely eliminate the interest of contemporary averages.

Also interesting is politics; here the confound is simply that the 19th-20th centuries have seen widespread partisan shifts in particular directions, which means age will correlate strongly with politics unless people are completely spineless. Here the evidence favors me not shifting my liberal libertarian beliefs, because that's the tendency of old people in general - to shift to be more liberal than their cohort began as: http://www.gwern.net/DNB%20FAQ#fn85

(This could just reflect pressure to conform by all the younger cohorts - but if you're willing to make excuses like that, the majoritarian/modesty argument goes right out the window in general!)