I don't like the undergravel filters. I find that the gravel gets stuck in them and makes them worthless anyway. I've also had them get stuck and then scratch the tank trying to get them out. use hang-on or internal filters.
Okay, I don't want to sound rude or not caring. But I keep my bettas in small unfiltered tanks without changing the water for a few weeks. One time, and I know this is bad, I didn't change the water for months(PLEASE DON'T FREAK OUT AT THAT). My fish are very active and happy. All I'm trying to say is that water changes really only have to be done every few weeks...
And I think you just don't know enough about fish. NO creature should have to live in their own filth that long. Would you wait to change a baby's diaper for days after they pooped? No, you wouldn't. So don't do it to your fish.
It releases ammonia, which builds up in the water. It doesn't take long for that to happen. They also release ammonia from their gills. That's why frequent water changes are necessary. Please don't get any more fish if you refuse to listen to reason.