Your post explains why it is nearly impossible to combine these 2 energy rings for those exact reasons:
Ideally you would want the broken ring too, but still the issue of mana management could make it more of a shore to use against enemies that deal 20 damage per turn, or enemies like the fire geckos or the repxecutiors which will break down your defenses making it pointless. Though, I do recommend the candle and the My First Wand coupled with a Necronomicon for this build to alleviate the issues posed by those enemies if anyone will ever be attempting a run using this build.
Correct, but the most reliable way to give the player rage is via the forge. In fact, passing by the forge twice will make that every hit the player makes gives him +2 rage, and if he really is that lucky he can increase this number again to +3 and then +4. The forge upgrades are almost a must-have for endless and the fact that only weapons and shields can receive them is why this is not a good build in the long run.
You can attempt a run with a ring of rage, but you will need mana and a way to recover it consistently. The most common book type item has a rarity of uncommon (with the Necronomicon being Legendary and the best book to pick) and the most common item that gives you mana automatically at the start of each turn is the robe which has a rarity of rare, but because it is an armor type, it cannot be used if the player is holding a Berserker's ring, so the only item in the entire game that gives the player mana automatically in this specific set-up is the frog totem, but because it is a relic you can only have one of them.
You may also consider getting a cap (+1 damage to wands), and the magic necklace that adds +4 mana whenever you kill an enemy with a wand, but it is all really cumbersome, speaking from personal experience.
