How could you make Westeros more democratic, or meritocratic, without pushing the nobility into rebellion? Give more power to Guilds maybe, let cities and their urban classes become more wealthy/powerful?

Well, democratic and meritocratic are not the same things; got to be careful when thinking about virtues and political systems, because a lot of people from 18th century liberals to the present day fox themselves by blurring those categories.

So I’m torn between my Team Smallfolk side and my historian’s side. My Team Smallfolk side says we go full Wat Tyler, let the nobility rebel, and then crush them like we’re Flemish artisans. My historian’s side says that revolutions can go backwards and that change is often gradual and long-term (but also that it often goes in a process of “punctuated equilibrium” where you have to push as far as you can in the moment, but always being careful that you push for what’s sustainable). 

I would say that you build on existing institutions: 

• First, institutionalize the Great Councils of Westeros, as a quasi-representative body that embodies an alternative principle of legitimacy beyond the right of blood or conquest, and which seems to operate under the principle of all lords being equal (that’s something you can build off of. (Likewise the Kingsmoot, the elections of the Night’s Watch, etc.) Eventually, build the Great Councils into something akin at least to the Tudor Parliament if not yet at the level of the Parliament of the 17th century. 
• Second, extend the tradition of “any knight can make a knight” and the quasi-revolutionary nature of the knight’s oath. On a cultural level, encourage storytelling about Ser Duncan the Tall and other knights who expressed their virtues by defying their superiors rather than obeying them. Expand the class of knighthood down into the elite of urban society by making guild masters, burghers, etc. knights. This should create a class of people who have something to lose from the old order coming back, who can mobilize other people to fight counter-revolution. Eventually, give all knights representation on the Great Councils – although the principle of “one lord, one vote” might have to shift to something more elective, because getting everyone in one room is hard enough already. 
• Third, restore the reforms of Aegon V, whatever they may be. Really work on enforcement, so that the law is uniform whether it’s under the king’s eye in the Crownlands or out in Dorne or in the far North or out in the Westerlands. Work to extend royal justice vis-a-vis the right of pit and gallows, perhaps compromising with the local lords by letting them recommend candidates for justiceships. Eventually, work to expand the idea that individuals and communities have inalienable rights – perhaps building off of the ideology of the Seven that we’re all children of the Gods, etc.