That's really a hard challenge, but let's try some ideas...
Any ideas of how this could be blow out of proportion and this useless track of land be used as a casus belli for a general war between the two giants of south?
Well, in 1895 the Brazilian president was already a civilian, Prudente de Morais, and he wanted peace after all the conflicts that happened during the government of Floriano Peixoto. I doubt he would go to war against Argentina, in a moment when he still had the opposition of a large part of the Army. We would need to change that first, putting other president from the Armed forces in charge. Unless Argentina declare war first, but I'm not sure if it would be possible.
Maybe, for a Brazilian declaration of war, we would need Cleveland not accepting the Brazilian proposal, which was the chosen by him. Maybe, if he had supported the rebells of the Navy in 1893, accepting them as beligerants, as they wanted, but not sending any material support, and so leading to their defeat as IOTL, the Brazilian government would be more anti-American (or at least anti-Cleveland), and he could have later a decision more pro-Argentina, causing an armed intervention (and even that would only happen if we have someone from the Army as president).
Secondly...how does the war develop? how good are the opposing armies? I know ours was good, but weakened by the Revolutions of 1890 and 1893, not to mention corruption and lack of practice... Besides, the terrain is...err... Ideas? thoughts? comments?
Well, the Brazilian Army was not good. I don't have the numbers of 1895, but in 1889 there were only 13.5 thousand men divided in 50 regiments. The problem for Argentina is that the majority of them (18 regiments) were based in Rio Grande do Sul, Santa Catarina had 1 and Paraná 3, so we have 22 regiments that could be sent fast to the front.
The real problem for Argentina was that in 1895 Rio Grande do Sul had just finished two years of civil war, when 1% of the population died. So there was a bigger presence of experienced troops here, and a lot of new arms bougth to fight the rebells. Add to this an invasion from Argentina and we could have the perfect excuse to unite the forces against a common enemy.
For the terrain, I would say that it works more for Brazil. It's a territory easy to reach from São Luiz Gonzaga and Santo Ângelo, where the army had troops based, and in the North the railway between Rio Negro - in the border of Santa Catarina and Paraná - and São Paulo was already completed. So it would be easy to bring reinforcements from São Paulo and Rio.
What works against Brazil is the incompetence of the military commanders, as the Rebellion of Canudos showed in 1896. So I'm not sure that Brazil could win the war, but that would be surely a nasty business.
