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[Rynn]

Rather than slow the ship down to build a new cylinder, you could send an advance party with a fast ship to build it as the generation ship sails past. This would be much more economical on fuel and propellant. You could even cobble the fast ship together from the engines of the generation ship (which aren't being used, after all).

Assuming you have the manufacturing technology to do so, not to build the smaller ship but to pack enough equipment and people into it to to get the job done. Neumanns in the early days were't as advanced (the need for supervision places a cap on how many can be deployed for a given job) but they were good enough for the colonies that did succeed. For a story it would be a fine line between having enough technology to be able to send off industrial seeds to harvest/transport resources and build more habitats and not having technology good enough to keep your current systems going. There might not be any overlap at all.