I think you and I have the same tank. The Aqueon 4g Evolve, babbling about only changin water 25% monthly (which is made up, but it's a nice tank).
Glad you muffled the filter a bit to help with flow as it is strong -- a 25W adjustable heater that's submersible fits in the back with the pump easy.
As for water changes, I do two 50% weekly (doing water tests before each time so I know how the cycles doing). I work a full-time job where I'm running around all day and dont get to sit down till I get home, so I understand not having the energy for frequent changes (despite that I have 11 tanks and 18 bettas currently xD ) -- anyways, the changes don't take too much time, and staying on top of those water parameters helps in keeping the fish healthy before it gets really sick. Like nipping it in the bud.
As for the cloudy eye, I'm not sure what to suggest. I avoid any products that have tea-tree oil in it. When in doubt, I check out the Betta Diseases sticky's at the top of this forum.
Sorry I'm not much help, just thought I'd pop in because I have actual experience with the tank and wc's for it.
Edit:: If you dont change the water, ammonia builds up and burns his gills and stresses them out, making them very ill and leading to death. Bettas are generally hardy, but the chances of him living longer are higher with more water changes. Not every betta dies, but he will definitely get sick, and may repeatedly get sick afterwards until eventually dying. In a month's time ammonia and nitrites and nitrates will buils, which are toxic to fish (like carbon dioxide is to us)