Some more thoughts:

… or, forego using a uniquely Xtian prayer.

This is two issues in one:

• christian: are there "universal" prayers? Jews, Christians, and Muslims seem to pray to the same god, but what about the other religions?
• prayer: As i already said, Atheists and Agnostics wouldn't need a prayer. I have only hearsay about Al-Anon, but they seem to stem from a monotheistic, or at least deistic tradition, because four of the "Twelve Steps" explicitly mention "God".

In a SciAm article published on (conveniently) Christmas 2013, they write:

The authors tested several possible explanations, but found statistical support for only one: people interpret prayer as a social interaction with God, and social interactions are what give us the cognitive resources necessary to avoid temptation.

So it isn't important what you ask for in your prayer, because it is the very act of praying which helps you, even if you know¹ you are talking to an imaginary friend.

What substitutions would you make?

As you probably can take from my previous post, I am more or less content with the current text :-)

what makes a good substitute

If I want to reword a text (or even just better understand it), I often translate it, sometimes forth and back. Which languages, doesn't matter much. Although I know neither Toki Pona nor Láadan, (nor does Google Translate :-)), but from what I know about them, they'd be my languages of choice for this project. This particular text has already been translated numerous times, so it seems better to check with dictionaries, anyway.

¹(Update): originally, I wanted to write "are certain" instead of "know", but I wanted to make clear that this is meant to cover even "full Level" certainty.