Found a game-breaker. The Fluffy Cotton (top left) gives two mana when you use a want, so the ethereal and first wands refill a mana when used. I have Ring of Doom. The only problem is getting block, but I still have some time (and a broken ring). Edit: Not as good as I initially thought. First "good" build and got exited.
This still seems very underwhelming to me given that the frog totem gives you 3 free mana every turn and you don’t have to juggle wands.
Maths: Each wand is (at least) 2 spaces and can be used only once per turn, so even with a non-wand mana sink, that’s 2 mana per turn for 3 slots instead of 3 mana per turn for one slot. Even the Wizard Cap seems better than Fluffy Cotton at 4 mana for 1 slot and 1 energy, but that depends on how much damage you are doing per energy.
With your 4 wands, that’s 8 mana per turn for 9 slots. It can never come close to the mana per space efficiency of frog totem.
I think the best case for it is stacking the AoE weapon wand with Ring of Doom, but that will quickly fall off in endless. I think it should be able to beat the first loop of the game, though.