Employing a minimal array of electroencephalography (EEG) channels for neonatal sleep stage classification is essential for data acquisition in the Internet of Medical Things (IoMT), as single-channel and edge-based features can reduce data transfer and processing requirements, enhancing cost-effectiveness and practicality. In this paper, we evaluate the efficacy of a single channel and the viability of a binary classification scheme for discerning awake and sleep states and transitions to quiet sleep. For this, two datasets of EEG signals for neonate sleep analysis were recorded from Children's Hospital of Fudan University, Shanghai, comprising recordings from 64 and 19 neonates, respectively. From each epoch, a diverse ensemble of 490 features was extracted through a blend of discrete and continuous wavelet transforms (DWT, CWT), spectral statistics, and temporal features. In addition, we introduced an innovative hybrid univariate and ensemble feature selection approach with multidomain feature fusion, a stacking-based ensemble classifier that outperforms existing work. We achieved 90.37%, 91.13%, and 94.88% accuracy for sleep/awake, quiet sleep/non-quiet sleep, and quiet sleep/awake, respectively. This was corroborated by significant Kappa values of 77.5%, 80.29%, and 89.76%. Using SelectPercentile, we devised three distinct feature selection mechanisms: one using DWT, one with CWT, and another incorporating both spectral and temporal features. Subsequently, SelectKBest was used to determine the most effective features. For our stacked model, we incorporated a trifecta of the ExtraTree model with variable estimators, a Random Forest, and an Artificial Neural Network (ANN) as base classifiers, and for the final prediction phase, ANN was implemented again. The model's performance was evaluated using K-fold and leave-one-subject cross-validation.