As moderators, we have a strong preference for scale, perspective, and believability which are better served by a character whose age measures in the thousands than in the billions. As a character who spent 4.5 billion years repeating one thing recursively, the Doctor would, believably, be defined by that moment alone; the rest of his existence being a rounding error at best. It somewhat stretches credulity, and if possible we prefer to avoid that.

As noted, this point is negotiable, if it's important to you to play the Doctor past that canon point. It looks to us like there are only a few lines of your app which rely on this episode, so it doesn't seem to require a complete re-write, if that's the point of contention. We do have other characters (Death of the Endless) who are similarly cosmic in age and perspective, so either way, this isn't a dealbreaker from our perspective.