"Proemptosis" Natural Recordings by Native Speakers
Prodearth or more commonly proemthosis, now preferred as proemPTHosis, spelled proemptosis in some texts, is a rare orthographic variant of prosopopoeia especially in Chaucerian English.
Proemstosis
I couldn't find any definition for "proemial" in my databases. However, I think you may be referring to "proem", which is a noun that means "an introductory part of a literary work, especially a poem".