This is a part answer to this question, specifically if research has been done for this problem. Also, some perspectives of a Maths and Physics teacher of over a decade experience. Somewhat ironically, I am going to start by making a parallel to a topic that is arguably an equivalent in the Sciences: Physics - as in my experience, I have seen similarities in terms of top=down vs bottom-up learning.
According to "Learning to think like a Physicist: A review of research based instructional strategies" (Van Heuvelen, 1991), many studies then have found that conventional teaching methods (bottom-up in a lot of places), in their use of "primitive formula-centred problem solving" fail to properly develop topic and subject related reasoning and problem solving.
The point here is that enquiry based problem solving, which can be considered as 'top-down' allows the student to learn the topics and concepts within a context, in doing so, they see how various topics link together, that may not be so apparent when working with formula-centred methods. A caveat here, it is absolutely critical that the students have some background knowledge and skills that could be used in their enquiry, these would potentially be enhanced through a top-down type of enquiry.
This is emphasised further in the chapter "Research on Teaching Mathematics: The Unsolved Problem of Teachers' Mathematical Knowledge" (Ball, 2001), who asset that the most common encounter with mathematics is a set of rules to be memorised, equivalent to the 'primitive formula-centred problem solving' model described in the previous article, resulting in the subject not only being misunderstood, but underappreciated. This is an advantage of a top-down approach, according to the article (and my own experience), where if the student starts with a query (from an article or unfamiliar question), then it turns into a mathematical challenge, rather than a pedagogical one.
Finally, a key point from the chapter "Learning to think mathematically: Problem solving, metacognition, and sense-making in Mathematics" (Schoenfeld, 1992), make several key points outlined above, and:
Present problem situations that closely resemble real situations in their
richness and complexity so that the experience that students gain in the
Learning to think mathematically, classroom will be transferable.
This includes taking an unfamiliar problem, and using skills and knowledge that they have to disassemble the problem to understand its components. Essentially, a great skill can be developed in the top-down approach - how to break down a big unfamiliar problem into its more familiar ingredients.
Hope this helps.