The edges of the Estes plastic nose cone are too square and could turn the interior body tube edges in.
A simple rounding of the base edges gave an better slip fit.
The BT-5 tube was longer than the wraps.
Both ends of the tube were trimmed down, just above the printed wrap ends. The nose cone was slipped into the tubes for support when cutting.
The remaining white tube was sanded down to the wrap ends.
I know, stick to the subject -
With the nose cone inserted in the bottom, the tube makes a good single note Pan Flute.
The 7" BT-5 tube plays clear, close to an F#.
Try this next time you have to entertain the grand kids. They'll think you're a genius.