I'm not sure about making Leliana the Divine... She does talk about freeing up the mages, which sure, Solas would agree with. However, she also talks about forcing change, and bringing the elves and the dwarves into the fold, because she believes this would bring peace. She goes on to say that "There are those who would cling to the old ways, of course, but they will see. I would make them see." That smacks so much of colonialism that I could not support her. I imagine her forcing elves, dwarves, and Qunari to convert from the elven pantheon, the Stone, and the Qun and join the Chantry. I do not believe Solas would support that. Well, except maybe for forcing the Qun to change.
Seriously though, forcing people to change their old beliefs (even if it was in the Qun) does not strike me as something Solas would support, with all the value he places on freedom and freedom of thought.
ETA: I was looking up info on how the Divine was chosen, and added up the points Cassandra, Leliana, and Vivienne would have received based on my choices... Either the wiki is missing some information, or I had a bug in my game, because Cassandra had 11 points, Leliana 21-22 points (I don't remember what choice I made for one of the Divine point-giving things listed there), and Vivienne -9 points, yet Cassandra became the Divine in my game. For which I am grateful.
I don't think softened Leliana would forcibly convert people. Hardened Leliana might.
Yes, she wants more people to turn to the Chantry, but I think she'd use her words to convince them, rather than forced conversion (which, incidentally, is how the Qun converts people... via force and brainwashing).
In all honesty, other than the force she uses to uphold her power, Vivienne is probably the best person to make Divine (my opinion only), simply because she is the moderate (surprisingly enough) option. Being a mage makes her a radical choice, it's true, but out of all three, Cassandra changes the least and Leliana changes the most about the Chantry and its infrastructure. Leliana's Chantry, which is open to all comers and opens the priesthood to men, elves, dwarves, and qunari, is in many ways ideal--but too much change often meets with resistance, and it's all too often the violent kind of resistance. Cassandra's desire to make things just go back the way they were can't succeed--we see where that led already. You can't tell people they aren't prisoners while treating them like prisoners. Sooner or later you'll end up with the same results: the templars will abuse their power, mages will be made Tranquil, and of course, mages will rebel. Vivienne offers increased freedom to mages who earn it--which is actually a logical solution even if it means they're still effectively prisoners. I'm not sure if she would still allow Tranquil--likely she would--but in many ways mages are so accustomed to being imprisoned that they have difficulty adapting. While plenty are pleased with freedom, plenty more miss their towers. Although I'm sure Solas would disagree with me vehemently on the grounds that freedom should be granted outright, not earned, I see Vivienne's leadership as less "the way things should be," and more a stepping stone on the path to a more Leliana-like Chantry.
Having said all that, even though I think Vivienne may actually be the best choice, there's no way I could avoid putting Leliana in power. Her entire story thus far seems to have been leading her up to it. And honestly, although I know her drastic changes to the Chantry aren't really wise, I can't disagree with her intentions. Again, I don't think she's going to force conversions (if I suddenly learn she has, my opinion will change for sure!). She just wants the Chantry to be more inclusive to those who already believe, and more welcoming to those who may wish to convert. She'll open the priesthood to everyone, not just human women. And as for those who want to cling to the old ways, I'm pretty sure that refers to the Chantry's old ways--the belief that the Maker abandoned everyone, the removal of Shartan from the Chant of Light, keeping elves and dwarves and qunari out of the various Chantry buildings when believers should be welcomed there regardless what shape they take.
I would be more fearful of Cassandra as Divine forcing her way than of a softened Leliana, who would likely lead by example and expect conversions to happen as they would. Cassandra is, let us not forget, the one who expects your Dalish Inquisitor to embrace one more god in the Maker, but then openly mocks and disparages your Dalish gods later on. Unless your Dalish Inquisitor was never much of a believer, that's incredibly insulting. Sure... take one more god, but remember he's the only real god and that makes you and Ameridan both complete fools, in the eyes of Cassandra. And even post-Trespasser, a Dalish has the right to remain faithful and believe that the disparagement of his or her gods is negative propaganda from Fen'harel and his followers, who have much to gain from you turning your back on the "rightful" evanuris gods.
Solas can deny it all he wants, but by some definitions he is in fact a god--he is ageless, presumably difficult to kill, and he is powerful beyond what anyone else alive is capable of being. If the other evanuris compared to him in power, they could also be considered deities. Even if you completely believe they aren't gods by any definition, the Dalish, even the Inquisitor, still have the right to their beliefs and faiths. At this point they are less involved in worshiping an individual and more some nebulous idea of that individual. Since they don't truly know who it is they are worshiping (as in, they are worshiping crafted identities rather than the actual flawed people), who is to say that they are not worshiping actual gods that, like the Avvar, they may have created out of their own belief? Or that may have existed all along, and taken the names of the people they worship as a matter of convenience? Let's not forget that the Avvar gods are spirits. But they very much exist, and one of the actual definitions of a "god," is a spirit. Some such gods are greater than others.
... What I'm trying to say is, if you believe Leliana with her disapproval of people backsliding and trying to keep elves/men/dwarves/etc out of the Chantry (and the Chant of Light itself, in the case of Shartan) is bad, then how is Cassandra better with her desire to change literally nothing, but keep people imprisoned (under the caveat that she'll just have templars be more careful about not oppressing the mages they keep caged)? And how is Cassandra's mockery of others' beliefs any better than Leliana's suggestions that the Chantry should be a place people WANT to come to?
Frankly I agree with Leliana's intentions the most, but I see Vivienne as a necessary step to get there. But both Cassandra and Vivienne are more likely to press Chantry beliefs on those who don't accept Chantry dogma--Cassandra, because she seems to believe that any other beliefs are foolish, and Vivienne because whether she has faith or not, an increase in followers is an increase in power.
And I think you have misinterpreted what Leliana meant by "old ways," because I still do not think she's referring to the "old ways" of the dwarves or the Dalish or the Qun. She's talking about the Chantry's old traditions, which are often senseless or have been the cause of senseless cruelty to others. Again, the persecution of elves and the removal of Shartan from the Chant were in no small part due to the Chantry's influence. Leliana remarks that although Varric is devout Andrastian, he won't go into a Chantry because as a dwarf he wouldn't be welcome there. Do you honestly think an elf would show up in a Chantry other than maybe a small alienage temple? And then who would preach to them? Elves can't be Chantry sisters. I'm reasonably sure she's also the one who says that the Chantry should lead by example, and that if they set a good example, people will convert to the Chant. Sure, she wants people to convert--she isn't going to force them (unless you hardened her, in which case she very well might). But she's highly religious and she might be put into position as a leader of her religion. Of course she wants people to convert--religions don't last long without followers!