DES - encrypt 3 times - DES(DES(DES, k), k'), k) - stronger than 2DES with 2 different keys?
As pointed out in the comments two key triple DES (without your complementary key condition) already has efficient attacks against it, going back to the 80's. See for example a detailed analysis in Van Oorschot and Wiener here which converts a chosen plaintext attack by Merkle and Hellman to a known plaintext attack.

Since 2 key 3DES is already weak, trying for sophisticated and complicated improvements based on the complementary key condition is likely not worth the effort.