I don't know i really think for betta better just do regular water changes. I kept my betta in the 10 gall and cycled and it didn't live long. Since i have them in 2.5 and 5 gall tanks, and i am doing full water changes they live longer. I saw you already have 2.5 gall tank,which is good size and you really don't need to have a filter. A lot of people here recommending it and i think it very good advice . I would say my bettas are very happy:)
Hey let me know if you need tips on disinfection i have very good link about that. And the link even show the video how to disinfect the plants. I hope you will decide to rescue another betta. Keep it in 2.5 gall though. You really don't even need / recommended the cycle 2.5 gall tank. You can just do 50% and one full water change a week to keep him healthy. Good luck, btw you doing wonderful job!