The funny thing is that he declared the war before the English equipment arrived, and that the fortress of Humaitá was built with support from Brazil.
Well, I think that for this to become feasible, and perhaps making a Paraguayan victorious, there should be a mechanism so that it can co-opt the provinces between rivers and corrientes, as well as Uruguayan rebels, which was the original Paraguayan plan. Unfortunately for the Paraguayans they were unable to co-op these allies.
EDIT: But it is good to remember that Paraguay resisted so much because of geography, Paraguay is in a place of difficult access and there were no maps of the region in the hands of the allies. After the fall of Humaita the war accelerated and soon Paraguay fell.
1) there was a weapons delivery from UK for paraguay that never arrived because brazil blocked the paraguay and Parana Rivers. If paraguay had won the naval battle of Riachuelo (and not simply win, but decisely win it) the deliver could have arrived.
2) Paraguay had a harsh marshy terrain that was unknown for the allies beyond the rivers banks and there were no maps, true.
But Paraguay has the merit of building an powerful defensive system in the areas known by the allies that was able to hold the line for two years and block the naval assets of the aliance.
Brazilians have the merit of conquering the paraguayan forts without much bloodshed.
After the major victory of the allies in the battle of Tuyuti, the biggest of the war, most and the best army of paraguay army was destroyed ( and could not be properly rebuilt because they had few reserve manpower)
All the paraguays could do from that moment was to hold behind their forts and hope the allies to front assault it in hopes of winning defending from a strong point.
And it worked in the beggining, the allies frontal assaulted the fort of Curupaity and suffered an devastating blow that paralised offensive operations for more than a year ( and de facto kicked Argentina and uruguay out the war, uruguay only kept a token force and argentina had to send its forces to fight rebellion that triggered after the defeat at curupaity)
Thats when Duque de Caxis was sent to lead the army, rebuilt it and adopted an strategy of encircle the forts of Humaitá instead of assault it.
The paraguayans were forced to abandon humaitá and built a second fortification in the doors of Assunção (angostura) that this time, they hoped, the allies would be forced to assault given there was no room for manouver this time.
In order to bypass it Caxias used the manouver of pissiquiri, he built an road in the other bank of paraguay river, which was an marsh considered unpassable, bypassed Angostura and used the fleet to cross the army the river betwenAssunção and the paraguayan army. Instead of going for the capital he turned back and attacked the paraguays armies from the back and destroyed it.