Localization is a key feature of future Sixth Generation (6G) net-works with foreseen accuracy requirements down to the millimeter level, to enable novel applications in the fields of telesurgery, high-precision manufacturing, and others. Currently, such accuracy requirements are only achievable with specialized or highly resource-demanding systems, rendering them impractical for more wide-spread deployment. In this paper, we present the first system that enables low-complexity and low-bandwidth absolute 3D localization with millimeter-level accuracy in generic wireless networks. It performs a carrier phase-based wireless localization refinement of an initial location estimate based on successive location-likelihood optimization across multiple bands. Unlike previous phase unwrapping methods, our solution is one-shot. We evaluate its performance collecting ~350, 000 measurements, showing an improvement of more than one order of magnitude over classical localization techniques. Finally, we will open-source the low-cost, modular FR3 front-end that we developed for the experimental campaign.