So here is the final result:

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Black bands are the original hand grips.
Blue bands are the new hand grips.
Shiny silver tube is the extension (actually I already had this tube; it was the pipe stand for a solar lawn light that had exceeded its useful life).
Quick-Release Button Connectors for Telescoping Tubing (one from McMaster Carr; the other was original to the paddle design) lock the tubing pieces together.

Not shown are shims:  One end was shimmed with a piece of plastic hand grip from an old set of free weights; the other shimmed with a wrap of duct tape not more than 2 layers thick)