Energy harvesting is becoming a preferred choice for future wearable embedded systems compared to batteries because of size, longevity, and maintenance convenience. However, harvested energy is intrinsically unstable. In order to overcome this drawback, non-volatile processors (NVPs) have been proposed to bridge intermittent program execution. However, the harvested power is limited even with multiple energy harvesters when they are in-door. Therefore, a near-threshold processor is ideal to maintain low power consumption. One of the biggest challenges in realizing near-threshold non-volatile processor is to provide a required high write voltage to non-volatile memories when there is a power failure and checkpoint is needed. In order to address this challenge, in this paper, we propose a dynamic converter reconfiguration for ambient energy harvesting-based NVPs to support near-threshold computing. We further investigate thorough optimization techniques to achieve high robustness in reconfiguration and checkpointing, high conversion efficiency, and low ripple magnitude. Experimental results demonstrate that the proposed techniques can significantly reduce the power consumption and improve the performance of energy harvesters and NVPs.