Hyperspectral satellite missions generate massive data volumes that are difficult to transmit and store, making effective lossy compression a key enabling technology. We propose SpectralNet-X, a transformer-based autoencoder for spectral-only compression of spaceborne hyperspectral imagery at a fixed compression ratio of 16. The encoder maps each spectrum to a low-dimensional latent code using a 1D convolutional projection followed by stacked self-attention layers with rotary position embeddings and cross-attention pooling. The decoder reconstructs full-band spectra through an upsampling stack and per-band affine calibration. To improve reconstruction fidelity and generalization, SpectralNet-X is first pretrained via masked-signal reconstruction inspired by SimMIM and then fine-tuned with a mixed objective combining mean-squared error and spectral angle mapper (SAM) terms using a scheduled weighting scheme. We evaluate SpectralNet-X on the large-scale HySpecNet–11k benchmark and in a cross-sensor transfer setting, where models trained on HySpecNet–11k are tested on PRISMA hyperspectral scenes. Compared to three compression autoencoders, SpectralNet-X achieves the lowest angular reconstruction errors while maintaining competitive distortion metrics and substantially reducing the fraction of spectra with large SAM outliers. This study evaluates learned spectral compression under a normalized post-correction setting rather than in an end-to-end operational onboard radiance-preservation pipeline. The experiments rely on L2A and radiometrically corrected products rather than raw at-sensor radiances, so narrow atmospheric absorption features and residual Fraunhofer-line effects are not represented as in a true onboard scenario. The presented results should therefore be interpreted as evidence for learned spectral reconstruction under a controlled post-correction setting, not yet as direct validation for operational onboard deployment.