A lot of times I use what I think you term as unclean language to inject some energy into the conversation. Without it I feel like the conversation dies, so I relate with my own story, or pass a half-judgement, do something to fire them up.
I don't know, it doesn't feel like the best solution, but it's the one I use, any thoughts?
Like many skills, learning to be aware is 80% of the work, 10% is the actual skill, and the remaining 10% is knowing when it's appropriate.
That's what works for me too. My experience tells me that just being aware of how much clean language I'm using and when I should and shouldn't be using it gets me to where I want to be. Being unaware, or trying to use as much as possible are, for reasons you mentioned, not the best approach.
Maybe the most interesting things about clean language is how little of it you actually need for it to be wildly effective. Applying just a bit when you sense someone opening up or being vulnerable is, in my experience, a loving way to receive that message gracefully.