The reality is that you cannot force such openings as black, but you can pick openings that may suit your style.
I really think that the Nimzo-Indian/Queens-Indian may suit your style very well. They will not get you queenless positions too often right out of the opening, but the nature of the Nc3 in the Nimzo, and it often getting exchanged resulting in doubled pawns for white, you will get a lot of strategically complex positions that have structural weaknesses to work against (usually in exchange for the bishop pair), and there is often a lot of maneuvering. In the Queens-Indian, you get the fianchettoed bishop you like, and nice control over e4, which allows you to try and chip away as the white center. I have also gotten a number of nice kingside attacks too against the white Kg1.
This has been my bread and butter opening pair as black against 1.d4 for decades, and I like the type of positions that you like. The theory is old now, but if you can get a hold of the book "Understanding the Queens Indian Defense" on eBay, it does a great job of teaching the underlying ideas. You can also study Karpov's games, as this was his main weapon as black during his peak years.
In the Nimzo take this famous game in the Huebner variation of the Nimzo. Of course, there are many variations, and you would have to learn more than just the Huebner.
[Event "World-ch27 Fischer-Spassky +7-3=11"]
[White "Spassky, Boris Vasilievich"]
[Black "Fischer, Robert James"]
1. d4 Nf6 2. c4 e6 3. Nc3 Bb4 4. Nf3 c5 5. e3 Nc6 6. Bd3 Bxc3+ 7. bxc3 d6 8. e4 e5 9. d5 Ne7 10. Nh4 h6 11. f4 Ng6 12. Nxg6 fxg6 13. fxe5 dxe5 14. Be3 b6 15. O-O O-O 16. a4 a5 17. Rb1 Bd7 18. Rb2 Rb8 19. Rbf2 Qe7 20. Bc2 g5 21. Bd2 Qe8 22. Be1 Qg6 23. Qd3 Nh5 24. Rxf8+ Rxf8 25. Rxf8+ Kxf8 26. Bd1 Nf4 27. Qc2 Bxa4 0-1