Micromesh Gas Structures (Micromegas) as readout of gaseous Time Projection Chambers (TPCs) are being considered in experiments investigating rare phenomena, like the nuclear double beta decay, solar axion detection and low-mass dark matter interactions, due to their good performance on spatial and energy resolution and operation stability. In addition, as they are potentially made mainly of radiopure materials like copper and kapton, they are appropriate for ultra-low background conditions. After a promising first study of the radiopurity of Micromegas readout planes, here results after dedicated development at CERN obtained from new radioassays, performed at the Canfranc Underground Laboratory combining different techniques, are presented. Activity of the isotopes in the lower parts of the 238U and 232Th natural chains has been constrained by analyzing the BiPo sequences using the BiPo-3 detector to be <0.064 and <0.016 muBq/cm2 respectively, while a lowest 40K content of 0.102+-0.030 muBq/cm2 has been determined by gamma spectroscopy using a HPGe detector; the latter value implies a reduction of a factor 34 with respect to the 40K activity quantified in the first analyzed sample. These results confirm the suitability of the use of Micromegas as extremely radiopure readouts for rare event searches.