Interesting question! Are there studies on the benefits of the more general edge cases: (1) Learning to program, regardless of language, and perhaps not even with maths as a primary focus, and (2) using software to "look at" maths, plot things, solve stuff, but more in the "graphing calculator" sense than in the "programming" sense. Both of these aspects may give you ideas about how to proceed here, and there must be some data on that already.
And as you said, there also needs to be a way to put these benefits in perspective and compare them with other activities, because school time is a limited resource.
(By the way, "traditional maths" can teach a very different perspective and skillset from computational thinking, so I really wouldn't throw either one overboard so quickly. You know... it's fine to enjoy the book and the movie.)
