When is God "Father" vs. "Dad?"

I am part of the "Spoken English Bible" team, which is tasked with producing a colloquial English OBT with a suite of oral translation tools. 

When is God "Father," and when is He, "Dad?" This was the question we recently discussed for 90 minutes in our monthly meeting. Around 15 people were involved in this conversation, ranging in age from 20s-70s, from varied home life experiences, and from regions spanning most dialect regions in the US. All but one of us used the term "father" in situations where (1) the formal role was more in focus and/or (2) more intimate expressions were not publicly appropriate. 

Here is where get things get messy. No two people overlapped exactly in all of the actual speech situations in which "father" would be more appropriate than "dad." For example, for some, (a) "dad" was only appropriate with family and close friends while, for others, (b) "father" would only be used in formal interactions (e.g. talking to insurance companies, police, a court testimony). While the room might roughly divide in half on such an issue, when we talked about the next concrete situation then the group (a) and (b) from the previous question would be roughly split again. By the end of the discussion, it was clear that no two people used "dad" in exactly the same speech circumstances. 

Needless to say, this makes it very difficult to set translation guidelines for when we should choose "Father" or "Dad."

How did this align with our community testing results? Our audience is secular American English speakers who are Millennials and younger. Many of them are offended that Jesus would call God "dad" because they think that indicates "too close of a relationship" and that "God doesn't get that close with people." 

So, we are rather stuck with the conclusion (a) that "dad" is a term that we should use in reference to God to communicate relational intimacy between the Son and the Father and (b) that we don't have clear guidance on when to use "dad" vs. "father" on a passage-by-passage basis. 

How have those of you working in languages with multiple terms for "father" dealt with this type of problem?