Electric charge fluctuations $χ_n^Q$ allow comparisons between theory and experiment, but are elusive on the lattice due to severe cutoff effects. We use a 4HEX action to obtain $χ_2^Q$ and, for the first time ever, $χ_4^Q$ in the continuum limit. We find disagreement with the hadron resonance gas (HRG) model, which we cannot explain with finite volume effects. We include light meson interactions in the HRG model via the S-matrix, reducing the tension for $χ_4^Q$, but worsening the agreement for $χ_2^Q$. We propose measuring the ratio $χ_4^Q/χ_2^Q$ at the LHC to investigate this tension.