Phase change memory (PCM) is rapidly emerging as a promising candidate for building non-von Neumann accelerators for deep neural networks (DNN) based on in-memory computing. However, conductance drift and noise are key challenges for the reliable storage of synaptic weights in such accelerators. We demonstrate, for the first time, conductance drift and noise mitigation by integrating a projection liner into multilevel mushroom-type PCM devices. While the projection liner has little effect on SET-state drift (crystalline phase), it substantially reduces drift for RESET states (amorphous phase) and improves the overall noise across SET and RESET states. Further improvement in drift is demonstrated by combining projection liner with a low-drift GeSbTe (GST) phase-change material variant. Lower drift and lower device-to-device drift variability for devices with projection liner are confirmed with large-scale experiments of over 1,000 devices. Moreover, we demonstrate using 10,000 projected PCM devices that tighter closed-loop programming distributions can be achieved, which is critical for in-memory computing based accelerators for applications such as DNN inference. Simulations show that the lower drift and device-to-device drift variability significantly increase the inference life span of PCM-based DNN accelerators.