I don't think our brain can conceive of something "beyond existence". Just because some religious people like to describe god as "beyond existence" isn't a good reason, imo, to believe that god therefore can't exist.
There's more options:
1. Religious people simply have come up with a suitably mysterious description of god that shouldn't be taken literally-- since it's humanly impossible to do so. In this case "transcending existence" means roughly "God exists but in a more marvelous and mysterious way than the rest of us do."
2. God really has a way to "exist" beyond "existence" and in that case, the mere fact that we can't conceive or it, or do not currently have the correct words to describe whatever the heck it is he's doing, also shouldn't be taken as evidence of his inexistence.
I think there should be better balance between transcendence and immanence. One saying God is completely independent and separate from the material universe where as the other says God is fully present in the physical world. Because transcendence should mean, as you suggested earlier with "greater than", that god would be independent but have the ability to transcend within the material world. So both transcendent and immanent. A god completely removed may as well be deism.