Okay, I confess that I don't really remember exactly what Jeff's avatar said, but here's my $.02 worth.
Your proposed policy says that "the use of the word God or any of the hundreds of other words that denote a "higher power" or any words that refer to an aspect of that higher power or a Prophet of that higher power may be used so long as the usage is in a positive manner and is not to be used evangelize a person's religious point of view." To decide if a statement of "I believe in Jesus" falls outside that guideline, I'd look at interchanging the word Jesus. If it said I believe in chairs I wouldn't be saying that I really want you to believe in chairs too. Granted religion is much more controversial than chairs.
If Jeff's avatar, or anybody's avatar or signature simply state that they believe in any God (or similar names as noted above) I think that it meets the letter of this policy. They would be simply stating their belief and are not saying that anyone else needs to agree with them, therefore not evangelizing. I agree with all that this is really splitting hairs and could lead us down a path where we don't really want to go. What if someone wants to post that they believe in Satan? Or anything that would probably mostly offend most of us? Let's face it, we have members who would accept this as a challenge to see how far they could push the limit before they are "censored" (actually, on any given day, most of the folks who can see this post are among those folks).
If this in the policy and meant to prevent avatars like Jeff's was, it would need to be restated. Do I know of a way to define what you are trying to say that would allow folks to say things like God bless, be blessed but restrict stating a personal belief, nope.
So, I guess that I'd leave the statement as written, wouldn't have asked Jeff to change his avatar and your signature is fine (of course, I think your signature is fine either way). I think that Screwed needed to change his name, GotWood might have (being a woodworking site, all I thought of was the milk commercial) and GotWood's avatar would have to be changed.
I know that I have asked that a couple of threads be deleted/modified but also feel that this issue will only be made more slippery by trying to define it any further. Sorry, I'm sure that my $.02 worth (probably at least $.05 worth just due the wordiness) probably doesn't help at all. It helps a lot