That's one fitting to use.
I also would've suggested fitting a tube inside or outside the bars and clamping it down; I'd've used something like seatpost clamps for that part. I have a few ideas for projects that involve such things to create the tube extensions I will probably need for steering stems and the like.
Another way I planned to do it was find some bars or other tubing (like bedside potty chairs) that are slightly smaller diameter, but not quite small enough to fit inside, and then cut a slit down the length of the smaller tube. Just make sure the slit is barely enough to allow the tube to insert inside the bars, so that it's edges come together inside, preventing it from loosening if lateral pressure is applied on the bars.
Hammer that down into the extension bars halfway, then hammer that assembly down into the original bars, using a tool from the inside if necessary to push on the internal slitted tube so it doesnt' slide further into the extension bars. No welding, and in theory can still be removed but would almost certainly never come out or shift on it's own.
