In this parallel, the Mauá Baron had a much better relationship with Dom Pedro II because he managed to join the masonry much sooner.
The baron was a politican, visionary, industrialist, and in this TL he managed to see clearly that slaves were a thing of the past, and that the only way for Brazil to grow was to create internal demand for high end services and jobs.
After a lot of political manouvering, he managed to create a massive railroad, conecting most of the Brazilian coastline and Sao Paulo and minas gerais.
Dom Pedro II in this timeline was in much better terms with Maua, and helped in all the way, using this industrial reforms to convince everyone of how much the monarchy was best suited to bring progress and reform than any revolution.
By the time the Paraguay war started, Brazil ha basically the same conditions it had in OTL, but because of the developed railroad, they managed to muster troops and equipament easier, also, there was a stronger sense of patriotism, which made the government give a little more resources to the army, instead of avoiding creating a huge standing army that could rebel.
After winning the war Dom Pedro II decided to use the army for an interesting purpose, he increased their pay, and ordered them to build works where no workforce was avaible, and ordered them to march into the amazon to build a massive railroad that would increase the effective area of productive land in the country by a sizeable margin.
By Imperial decretem Mauá was ordered to organize the building of this massive railroad system, and people from all over the country are being hired in what is truly Brazil's industrial revolution.
Most of the workforce is slaves, but slave trade is long gone, some of the slaves that fought in the war were granted freedom, and Mauá had the interesting idea of creating this concept of working army, most of which are slaves, but paid a small salary, Brazilian industrialism is making the USA scared, and while the economic boom is helping supply USA demands for brazilian exports, the USA would rather not have such a thriving economic power in south america.
the Year is 1889 Maua has died a few months ago after being ill, without his massive intelectual and capitalistic support, the conservatives ousted Dom Pedro II after the abolishment of slavery and Brazil was entered in a massive civil war, between the developd middle-south and conservative-slave holding north, probably fuelled by a lot of spyonage.
Needs some work, but I think it has potential.
Anyone has input ?