The H system (Q3505590) and X system (Q3497763) are two systems for writing Esperanto without diacritics.
They have the official language tags eo-hsistemo and eo-xsistemo respectively, so there is no reason to use private use subtags.
L43385 (ŝi/shi/sxi) and L43386 (ĝi/ghi/gxi) are two examples of where the language tags would be used.