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Exceptional points (EP) are non-Hermitian spectral degeneracies where both eigenvalues and their corresponding eigenvectors coalesce. Recently, EPs have attracted a lot of attention as a means to enhance the responsivity of sensors, via the abrupt resonant detuning occurring in their proximity. In many cases, however, the EP implementation is accompanied by noise enhancement leading to the degradation of the signal-to-noise performance of the sensor . The excess noise can be of fundamental nature (due to the eigenbasis collapse) or of technical nature associated with the use of amplification mechanisms utilized for the realization of EPs. Here we show, using an EP-based $\mathcal{PT}$-symmetric electromechanical accelerometer, that the enhanced technical noise can be surpassed by the enhanced responsivity to applied accelerations. The noise due to eigenbasis collapse is mitigated by exploiting the detuning from a transmission peak degeneracy (TPD), which forms when the sensor is weakly coupled to transmission lines, as a sensitivity measurant. These TPDs occur at a frequency and controlled parameters for which the bi-orthogonal eigen-basis is still complete and are distinct from the EPs of the $\mathcal{PT}$-sensor. They also show a slightly enhanced detuning rate compared to the typically utilized EPs. Our device demonstrates a three-fold signal-to-noise ratio enhancement compared to configurations for which the system operates away from the TPD.