The groups I have been to all have used the Our Father or the Serenity Prayer (which invokes the "Lord.") These are both definitely religious (and Christian)!
Maybe its time to find some spiritual affirmation or mantra --or rewrite of the Serenity Prayer omitting the work "Lord"--so that meetings can be truly non-denominational?
And if a "god of our understanding" is just a "higher power," why not get rid of the word "god" and replace it with "higher power"? While I think for many people in 12-step programs it IS a spiritual rather than religious program, the actual words used are indeed religious ones.
Why not make them strictly spiritual and strictly non-religous instead?