At the end of the day it doesn't really matter who you give it to since it is doesn't change anything. Given the amount of ancient elven history we turn up, I doubt the Dalish are going to be that bothered about the Red Crossing revelations, beyond the token peace offering that they do give. It seems to me that the stuff about the evanuris is way more significant.
Likewise the Chantry. Their reaction is only to be expected; they will simply use it to reinforce their propaganda about the Exalted March on the Dales. Given the reaction when Divine Leliana decides to restore the Canticle of Shartan to the Chant, it is clear the Chantry as a whole does not like anyone suggesting that Orlais annexing the Dales was contrary to their prophet's intentions. I find it amusing that Leliana has decided to restore it when WoT2 has revealed it is likely not based on the actual events anyway.
The thing is, I assume that everyone simply stuck their heads in the sand over the Solas revelations because the nobility and the majority of the Chantry are not going to be happy admitting that Fen'Harel is real and that he and not the Maker created the Veil. This is what I find so odd about DAI because what is revealed about elven history is that for the most part the Dalish got it right, with the exception of the bit about humans, but what with the history of Andraste we find around the place (and in WoT2), plus the whole history of the Titans and the evanuris, it makes the visions of Andraste and the claims about the Maker pretty much redundant. Yet there is never the opportunity to go to the Chantry (or the Dalish for that matter) with everything we found out, which are way more significant than Red Crossing.
I'd quite like there to be some character in the next game who specifically goes about preaching about the true history of the world but is denounced as a heretic, with the PC able to decide if they want to support their efforts at revealing the truth or not. Then again, if we are going to Tevinter, may be there will be a big reveal about what really went on back in early human history.