Cat tower replacement part

I have a bigger cat that loves being aggressive on the top of our cat tower. Needless to say he broke this piece off. I designed this in Tinkercad and it fit in the cardboard barrel and the nut should be forced down in the hole. This helps the nut stay wedged in there making it easier to screw back in place. I will say that this did not help supporting the free standing piece so I exchanged this with another one and it has been in place for almost 5 months. I should also mention that I used hot glue to hold this in place.

*edit- This has been in place for a year now and is still holding strong!