We present a rapid and reliable deep-learning-based method for gravitational-wave (GW) signal reconstruction from elusive, generic binary black hole mergers in LIGO data. We demonstrate that our model, AWaRe, effectively recovers GWs with parameters it has not encountered during training. This includes features like higher black hole masses, additional harmonics, eccentricity, and varied waveform systematics, which introduce complex modulations in the waveform’s amplitudes and phases. The accurate reconstructions of these unseen signal characteristics demonstrate AWaRe's ability to handle complex features in the waveforms. By directly incorporating waveform reconstruction uncertainty estimation into the AWaRe framework, we show that for real GW events, the uncertainties in AWaRe's reconstructions align closely with those achieved by benchmark algorithms like BayesWave and coherent WaveBurst. The robustness of our model to real GW events and its ability to extrapolate to unseen data open new avenues for investigations in various aspects of GW astrophysics and data analysis, including tests of general relativity and the enhancement of current GW search methodologies.