The thing is, the eighteenth century saw the Bourbon Reforms which created new Viceroyalties- and even they were too large to effectively govern.
There's two fundamental problems, I think:
1. The tyranny of distance. A state that controls all or most of Spanish South America probably couldn't be physically governed in say, 1820. The infrastructure just isn't there. The roads don't exist, the bridges don't exist, the open mountain passes don't exist and perhaps most importantly the economies of the different areas don't actually interconnect that much- they're far too dependent on Spain and other overseas ports.
2. The persistent argument in the newly independent states between Federalism and Centralism took decades to settle. I think that the largest possible states would have to be federalist- but even if you manage to settle the argument in any one legislature in favor of federalism, what's to stop the argument flaring up again ten years later? That happened again and again.
Let's say that the hypothetical 'big countries' you can get out of Spain's New World colonies are:
1. Some kind of unified La Plata. So that's Argentina, Uruguay, probably most of modern Paraguay and maybe much of Chile if you can somehow overcome the obstacle of the Andes. A little bit of Bolivia, maybe.
2. Gran Colombia, or more properly just Colombia. Colombia, Ecuador, Venezuela, Panama- maybe a little Peru and Bolivia. Conceivably the Dominican Republic.
3. An Andean territory consisting of areas too hard to govern from the South or North. Peru, Bolivia, perhaps a bit of Paraguay, maybe some of Ecuador, probably northern Chile.
4. It's not South America, but for completion's sake- a Mexico that includes Central America and perhaps some of the Caribbean. Also, of course, the lost territories in the North.
Trying to keep any one of these together was beyond the best efforts of some very talented people in our timeline. Trying to unify even two of them was never a feasible possibility.
I think if you want a timeline with a powerful, unified Latin American state it's better to focus on a single area.