More efficient way to make multiple keyframed objects move at once?

There is the new Text: Typewriter filter, but judging by your screen capture you are looking for more animation (bouncing characters).
So your method is currently the way to do it in Shotcut. You could do it on one track (14 text filter on the clip) but that wouldn’t be much easier or faster to do.

Related discussion > This post by @jonray:

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