My original sentence says "stray" not "stay".Neither deviate nor stray would suggest to me any return to the original plan. If he deviated, it says to me that he deliberately changed the plan. If he strayed, it says to me that he sort of wandered away from the original, perhaps only a little. Either of those words would mean that he departed from the plan. (Think of someone walking on a path and deviating or straying from it.)
If he stayed with the plan, as your original sentence says, then he did none of those things.