FYI, the 9/32" bit is .2812" vs the 7mm bit that is .2756". You will want to use thick CA for the tube, or (and I prefer)Gorilla Glue. GG expands greatly to take up the gap, but it does take some time to set up. I let mine sit overnight. Also, as the GG expands, it can cause the tube to slide out. You can check the blank and push the tube back in every 1/2 hour or so for the 1st couple hours, or use a rubber band stretched over the blank lengthwise to keep the tube from sliding out. I do the rubber band and haven't had a problem with that.
I always use a 9/32" bit unless I am turning a custom centerband, then I use the 7mm bit for a bit tighter fit over the transmission.