I think the best way to build the culture is try to at the best you can show the value and do it yourself initially. Whether that's usability testing, user interviews, surveys. Like Amy said below, you can then present out. The one thing I've seen that is the most valuable is showing video interview or usability footage, typically that brings an A-HA moment.

Bazinga. I was thinking you were going to say that you work primarily in code and do it that way so at least even structurally speaking you can reuse the prototype code and save time there. Funny video tho. =)

Although the video is funny, I get it. How do you quickly demonstrate ideas without spending time IMMEDIATELY in a design tool or in code?