I feel like you just said that English has complicated spelling both because of its borrowed words and its native words. I think this could be shortened to "English has complicated spelling because of the spelling of its words." Or even "English has complicated spelling."
There is no one particular subset of English you can exclude to simplify its spelling. I don’t really know what you classify as Old English, but whatever Simplified English is, it is highly unlikely it excludes Old English as traditionally defined, as the majority ofthemost commonly used words - italicised here - havesuch heritage. The spelling of such words is probably not the most troubling part of English orthography anyway.