Subglottal air pressure is a critical physiologically-based parameter that reveals fundamental pathophysiological processes inpatients with voice disorders. However, its assessment in both laboratory and ambulatory settings presents significant challenges due to the necessity for specialized instruments, invasive procedures, and the impracticality of direct measurement in ambulatory contexts. This study expands upon previous efforts to estimate subglottal pressure from portable, lightweight neck-surface acceleration signals using a physiologically relevant model of voice production combined with machine learning techniques. The proposed approach employs a neural network architecture initially trained with numerical simulations from the voice production model, which is subsequently refined through a domain adaptation strategy from synthetic data to in vivo laboratory data. This proposed method provides a means to create subject and group-specific refinements of the original neural network. For comprehensive comparisons with previous methods reported in the literature, the proposed approach is applied to both normal and disordered voices, including cases of unilateral vocal fold paralysis and phonotraumatic and non-phonotraumatic vocal hyperfunction. The study is divided into two datasets, encompassing a total of 135 participants. The in vivo recordings consist of synchronous measurements of oral airflow, intraoral pressure, and signals from a microphone and a neck-surface accelerometer. Each participant was asked to utter/p/-vowel syllable gestures with variations in loudness, vowels, pitch, and voice quality. Compared to previously reported approaches, the proposed method results in subject-specific models that achieve over a 21% improvement in the estimation of subglottal pressure, as measured by root mean square error. These findings underscore the effectiveness of a non-linear, subject-specific regression approach in enhancing the estimation of subglottal pressure from neck-surface vibration signals.