[bioblitzkrieg]

I was under the impression that heidelbergensis originated in africa, and from the branch that migrated into europe through the middle east, thus sprang the neandertal, and from the branch that remained in 'east' africa archaic homo sapien emerged, with both neandertal and sapien sharing a commong heidelbergensis ancestor between 300,000-500,000 years ago.

But if like you said, Heidelbergensis originated from Europe with an ancestral migration of antecessor from africa, how would the timetable for sapien-neandertal divergence be able to exist, as the species before heidelbergensis 'antecessor' would therefore have to be the last common ancestor between sapien and neandertal, which seems too far back in time, unless your hypothesis also mentions homo sapiens as originating in europe alongside thier heidelbergensis ancestors or sapiens originating from another hominid that was heidelbergensis like in east africa.

though in a multiregional Sapien hypothesis, this answer could get quite complex, but please try to clarify, its highly interesting.