Either get a smaller filter or fix that one.. turning a filter on and off will be harmful as it will push out all the dead/bad bacteria that was gathering in there. Panty hose tied to the intake will help keep his fins out. Also, if you are using a filter, you don't have to clean out the tank that often. Tanks can be too clean just like they can be too dirty. 1 50% water and 1 50% substrate cleaning once a week will be more then enough. Some may even say it's too much and I would do whichever you feel is comfortable. But wouldn't do more then that.
Welcome and good luck with Nova, he sounds like a fun one. Grats on getting the betta bug!