Your post explains why it is nearly impossible to combine these 2 energy rings for those exact reasons:
- Other than the bricks and broken ring all of the items you have mentioned have an uncommon, rare or legendary rarity including the energy rings themselves and regardless this is not a viable strategy in the long run due to endless' scaling.
- The scaling issue is particularly true for the Teddy sword because the Teddy sword cannot be upgraded at any forge and ignore useful items like the gems since it is not treated as a weapon by the game, but I think you are aware of that already.
- Out of the entirety of your comment I think the brass knuckles strategy could eventually be the most fruitful if paired with multiple "wolverine gloves" to quickly kill all the enemies simultaneously and much more quickly.
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.