You set up a false dichotomy. An omnipotent God may want His existence accepted by faith based on evidence with some room for doubt. He wants you to have enough to believe, but not so much that you have the overwhelming feeling that He is constantly looking over your shoulder.
Uh-uh, doesn't work, and here's a few reasons why it doesn't. First, you say "An omnipotent God may want His existence accepted by faith based on evidence with some room for doubt."
This can only be the case if the god doesn't understand that a belief is held either for good reason or not. Surely an omniscient god is smarter than that.
An omniscient god knows precisely the level of evidence necessary to compel belief. That god either will or will not provide that level of evidence. If he provides it, belief is compelled. If he does not, the proposition must be accepted on faith.
Second, you say "He wants you to have enough to believe. . . "
OK, then, if He does want me to have enough evidence to believe then he will provide enough evidence for me to believe. An omniscient god will know exactly how much evidence is necessary. It's slightly ridiculous to believe that anyone who has been provided with enough evidence to believe in a god that can provide eternal life or eternal d--nation, will
choose to disbelieve in such a god
despite the evidence if it means eternal d--nation. For what possible reason might such an unreasonable, disastrously harmful decision be made?
Christians cannot have it both ways. Either one accepts that a proposition is true by virtue of evidence or one does not. If one accepts that a proposition is true by virtue of evidence, then faith that that same proposition is true is entirely unnecessary.
Third, for what possible reason would god desire that it be difficult to know that He exists? For what reason would a god choose to make himself or herself obscure?