Earlier quoted context omitted.
Щ is indeed read as "sht" in Bulgarian, but in Russian it would be read as a softer "sh" or mix between "sh" and "ch". If anything, maybe it can just be dropped in favour of plain "sh"?
From Ukrainian it gets turned into "shch". Which IMO sounds about right. Mainly because sh and ch are shorter sounds in English (ch can also be a little hard), but shch gets the point across.
Speaking as a Russian, I think that "shch" is close enough for an international conlang. It's not a sound that's particularly easy to learn or explain.