I've gotten to Womb II, however, and my build seems to have stopped changing.
That means you've depleted the item room pool, and now you're perpetually getting Breakfasts. I'm gonna guess your red heart containers were maxed out too, right?
Can the D4 or D100 give me Godhead?
The D4 and the D100 can only reroll your items into items from the item room pool. Since Godhead is an Angel Room-only item, you will never reroll into it.
Also, I want to clear up a misconception: You CAN get items that you haven't unlocked yet through D4/D100 rerolling. For example, you can get the Mind, the Soul, and the Body with the D4 without ever having unlocked the Lost.
EDIT: I'm getting conflicting information about the D4 (and therefore the D100 as well); the official wiki states that it can only reroll into item room items, while the BoI Cheat Sheet says it will reroll each item into another item from the same pool. I personally don't recall getting angel room items with the D100, but I'll double-check with Reddit to be sure.