I don't know if this is the same family, but I did find this document:
Requête pour élire un tuteur aux enfants mineurs de feu Jean-Éloi Gagnon, cultivateur de Saint-Jean-Port-Joli, comté de Devon, et de Marie-Thérèse Dessaint (Desaint) dit Saint-Pierre . - 9 août 1810
This is the translation from a free online translation:
Request to elect a guardian to the children minors of fire John éloi Gagnon, farmer of Saint-Jean-Port-Joli, county of Devon, and of Mary thérèse Dessaint (Desaint) dit Saint-Pierre. - August 9 1810
I checked the map and Riviere Ouelle is about 30 km from St-Jean-Port Joli. It's feasible that your Eloi Gagnon (1803) is one of the children mentioned above - might be worth investigating.
If the above group is part of your family, there are 2 documents available that can be ordered from the Laval University Archives (they will be hand written and in french - very difficult to read).
I could not find any other documents. If you want to try, this is the page I was searching on:
http://pistard.banq.qc.ca/unite_chercheurs/recherche_simple Just type what you want and hit `rechercher'.
I tried "Joseph Belzil", Belzil + Cacauna, "Eloi Gagnon" and "Gagnon dit Belzil". I found a lot of documents around 1920, and one from the 1700s, but other than the one I mentioned, none from the 1800s. With the information that you have, you may have better luck. Try the mother's name, siblings, wife's, etc. Also, try misspellings, as they relied on phonetics for a lot their spellings.
I have found that with this search engine, you have to try every combination you can think of. I have found documents that when I searched for a particular person, nothing came up, but when I searched his wife, it came up and had his name. It all depends on what was added to the search engine.
However, it's worth trying this site for every person in your tree in Quebec. I have found arranged marriages, wills, land transfers, sales contracts, lawsuits, orders of servitude, and more.
Sorry I couldn't do more.