Integrated nonlinear microring resonators are promising sources of bright twin-beams exhibiting intensity difference squeezing. To take advantage of the noise reduction of these quantum states, many applications require high squeezing levels. However, the attainable on-chip squeezing is constrained by the ratio of intrinsic to coupling loss, which is strongly related to design and fabrication limits. Here, we demonstrate a silicon nitride microring resonator engineered to enable a set of periodic strongly overcoupled resonances from which the estimated on-chip intensity difference squeezing is 11.8 dB, exceptionally high for an integrated device. Due to significant setup loss, we directly measure 1.4 +/- 0.2 dB of squeezing, corresponding to an on-chip level of 9.2 +/- 5.1 dB. In addition, the new, to the best of our knowledge, design inherently suppresses mode competition in the modes surrounding the twin-beams, enabling a constant high squeezing level up to moderate powers. These results represent a significant step toward the miniaturization of integrated devices whose performance benefits from surpassing the quantum noise limit using squeezed states, with particular relevance to sensing applications.