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There is only one example I can think of, but I am looking for an alternative.
Scene is a character deciding that a discussion isn’t going towards the conclusion he is looking for, so he suddenly decides to “switch gears.”
“Change tactics” could also apply but it is not what I’m looking for.
Some suggestions:
You appear to be looking for a Path metaphor. "Changing the subject" is usually interpreted as changing the direction of a conversation. So any term that indicates motion along a designated Path will be interpreted that way.
You see it in taking a tack, which means altering the direction of a ship by maneuvering the sails, switching/shifting gears, which means altering the speed of a machine, often preparatory to altering direction, and in deflecting, which usually refers to the conversation as moving along a channel or road.
Get the metaphor set up in your mind and then use phrases that it suggests.
Maybe reading Lakoff and Johnson would be a good idea, too.
Pivot works well in this context. From Merriam Webster
4: a usually marked change
especially : an adjustment or modification made (as to a product, service, or strategy) in order to adapt or improve
