Regular wood glue. The strip is thin cardboard tubing, so asymmetrical weight distribution shouldn't be an issue. At the time, I decided to do a LJ II clone from the original Centuri plans because the Estes kit was kinda expensive. Cut down a BT-100 coupler. I'm in the process of stripping the home print decals and paint to apply John Pursley's Accur8 skins for the LJ II, but here's a couple of pics:
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And since you mentioned the Estes Mercury Atlas, here's my clone:
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Found a couple of 3.5" dia. circular cardboard boxes with caps for carrying accessories. Wish I could remember the company's name. When I deconstructed the ends I found it was double lined, so used the inner liner as a coupling, and the end caps as bulkhead/centering rings. Decals were from Sandman. No longer making decals, but I think Mark Hayes at Stickershock23 can do it. Display capsule and tower from Kevin Cespedes at Shapeways (Aerobotix?). Balsa flight capsule and bt-4 tubing and nose cone for the tower from erockets. Tube walls are thick, so rocket is pretty heavy. Did this before I learned about the split tube technique. It may just remain a shelf queen. If you are considering doing a project like this, suggest you build a Dr. Zooch Mercury Atlas first, to get some good spoofing ideas for the details on the rocket.