Channel state information (CSI)-based fingerprinting via neural networks (NNs) is a promising approach to enable accurate indoor and outdoor positioning of user equipments (UEs), even under challenging propagation conditions. In this paper, we propose a positioning pipeline for wireless LAN MIMO-OFDM systems which uses uplink CSI measurements obtained from one or more unsynchronized access points (APs). For each AP receiver, novel features are first extracted from the CSI that are robust to system impairments arising in real-world transceivers. These features are the inputs to a NN that extracts a probability map indicating the likelihood of a UE being at a given grid point. The NN output is then fused across multiple APs to provide a final position estimate. We provide experimental results with real-world indoor measurements under line-of-sight (LoS) and non-LoS propagation conditions for an 80MHz bandwidth IEEE 802.11ac system using a two-antenna transmit UE and two AP receivers each with four antennas. Our approach is shown to achieve centimeter-level median distance error, an order of magnitude improvement over a conventional baseline.