With the IceCube-Gen2 observatory under development and RNO-G under construction, the first detection of ultra-high-energy neutrinos is on the horizon making event reconstruction a priority. Here, we present a full reconstruction of the neutrino direction, shower energy, and interaction type (and thereby flavor) from raw antenna signals. We use a deep neural network with conditional normalizing-flows for the reconstruction. This, for the first time, allows for event- by-event predictions of the posterior distribution of all reconstructed properties, in particular, the asymmetric uncertainties of the neutrino direction. The algorithm was applied to an extensive MC dataset of ’shallow’ and ’deep’ detector components in South Pole ice. We present the reconstruction performance and compare the two station components. For the first time, we quantify the effect of birefringence on event reconstruction.