Frames of Mind.
Sounds like K is trying to protect his wife from discomfort, and I have respect for that; he loves her, has history with her, and wants to make sure she's taken care of. Those are good qualities, and definitely deserve respect, but the conundrum is that you want to move things forward before his wife might be ready for that. No one person needs to suffer while other people are getting what they need/want - it's got to be a balance to stay healthy.
It seems like the communication doesn't need to happen with your partner, but rather your partner's wife. Have you talked to her, and asked her if it's something that she's open to the idea of? Have you shared your feelings with her, and asked her to do the same with you? Are you building trust, respect and a friendship with her on your own?
In my opinion, it can't all be one person's responsibility to move a relationship forward, and it's not the relationship structure that makes moving a relationship forward impossible. It's the communication, respect and consciousness of all of the involved members that creates healthy, happy dyas/vees. You're not just in a relationship with K - he is attached, and part of being a good metamour is having emotional maturity, concern for, and community/communication with his wife.