http://www.piyut.org.il/tradition/english/2684.html?currPerformance=3487
would this countis the way teimonim pronounce the qadheesh. and this is audio evidence/proof of how to pronounce the hei in the word shmeih. although op was adressing ashkanazim, i think this should fit in here quite nice as ani believe that this is the most proper way of pronouncing the word and how to pronounce loshon haqodhash as a whole. so not only does it answer? the op in that it doesnt sound like a eh sound or any other sound he mentioned. it has its own distinct sound which i believe whole be adopted by the klal as it was pronounced in the days of old