I would appreciate a few links to papers which do that, just to understand what you are talking about.

Most of Dan Dennett's work adopts the methodology you endorse, and as a bonus, it is usually very readable. A good example is the pair of papers, True Believers and Real Patterns.

Since you're a GR guy, you may enjoy the work of David Malament and John Earman, both of whom have written a lot of interesting stuff on foundational issues in GR. Try this paper by Malament. The first two sections are basically just survey, but in the third section he presents some of his original work, with references to papers where he discusses the issues in more detail.

Huw Price (one of the founders of the Centre for the Study of Existential Risk at Cambridge) has done a lot of cool work on time, among other topics. Examples: this paper and this paper.

Philip Pettit is a political philosopher who uses social choice theory to address philosophical questions (in the tradition of Rawls, whose Theory of Justice is an excellent example of hacking at the edges). Many of his papers are worth reading. Here's an example.

Christopher Hitchcock does good work on causation. Here's an interesting paper he co-wrote with Joshua Knobe on how our judgments about causation are tied up with normative notions.