Except they’re not; the 6-way isn’t a model I’d consider designed for MoCA. Based on the attached diagram, I’d consider shifting to a 2-way plus 4-way splitter configuration, instead (ex: Antronix MMC1002H-B + MMC1004H-B), with a 70+ dB “PoE” MoCA filter installed directly on the 2-way’s input port to maximize the reflective benefit. The top-level 2-way would connect to the modem location and the secondary 4-way splitter.
The Picolink splitter should be fine, given it shipped with your adapters, but it would be worthwhile ordering a replacement for it, as well, as a precaution. (Order from somewhere with a good return policy.)
Separately, you could take a pair of MoCA adapters and connect them at each end of a given in-wall run to check the MoCA stats (get the PHY rates) for each coax line, to see if any of the runs demonstrate inferior quality. If so, open the wallplates and check the termination quality for the cabling; you can test with the wall outlets bypassed, as well, to rule out a coax outlet as the issue source.
p.s. The PHY rates table shown does seem to indicate an issue with MoCA adapter #1, with the rates in the vertical column associated with adapter 1 all showing well below the preferable 3500-3600 range. Pretty odd for the diagonal “GCD” rates to be so low, as well; these are typical vs Lou in the 600-700 range.