We don't have synonyms for glossolaly yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are glossology, glossolalia and glossolalic.
(n) :
Archaic form of glossolalia. [Speaking a language one does not know, or speaking elaborate but apparently meaningless speech, while in a trance-like state (or, supposedly, under the influence of a deity or spirits); speaking in tongues.]
(n) :
Archaic form of glossolalia. [Speaking a language one does not know, or speaking elaborate but apparently meaningless speech, while in a trance-like state (or, supposedly, under the influence of a deity or spirits); speaking in tongues.]