There is a plugin named "ParentHoldLink" (part of Essentials) that solves this specific problem. Put the plugin onto each of your CUAs (CustomUnityAsset) and follow the instructions in the plugin UI. Find it here:
Your most essential MacGruber tools in a convenient single VAR package. Note that you can download older versions of this plugin for free from here. AudioReverb Adds an Reverb filter effect to the audio source you place the plugin on. It's...
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There is also a plugin named CUAManager (or something like that), which is specifically for managing Person attachments that are CUAs. However, I have not used it myself and don't know it solves your particular problem (but its likely)