Subglottal air pressure is a relevant physiologically-based feature that describes key underlying pathophysiological processes in people experiencing voice disorders. However, the assessment of subglottal pressure in both laboratory and ambulatory settings presents challenges due to the need for specialised instruments and invasive procedures. In a previous work, we introduced a promising method to estimate this feature from neck-surface acceleration signals, leveraging an approach that combines a synthetic model of voice production, notable for its high physiological relevance, with a neural network-based regression. In the search for more accurate subject-specific models, this study builds on that previous work refining the neural network regressor, which was initially trained only with simulations from a synthetic voice production model. The refinement is carried out following a domain adaptation strategy from synthetic to in vivo laboratory data, resulting in a better estimate of the subglottal pressure. The in vivo recordings correspond to synchronous measurements of oral airflow, intraoral pressure, and signals from a microphone and an accelerometer. The methods are applied to normophonic voices and others with disorders, such as unilateral vocal fold paralysis, and phonotraumatic and nonphonotraumatic vocal hyperfunction. Each participant was asked to articulate /p/- vowel syllable strings varying the loudness, vowels, pitch, and voice quality. Compared to approaches previously reported in the literature, the method presented leads to a set of subject-specific models that yields improvements over 21% (root mean square error) for the estimation of the subglottal pressure. These findings highlight that a non-linear subject-specific regression approach can be an effective method to improve the estimation of the subglottal pressure from neck-surface vibration signals.