To add to the questions you've already been asked, are you confident that your internal domains are properly identified, and that your Marketing Channel Processing Rules are accurately defined? I ask because of this statement from your original question:
"An artifact of this seems to be a large percentage of transactions being misattributed to our internal session refresh channel in Adobe Analytics."
Are there other signs that point to this being a cookie/ECID issue, or is this the inflated Internal Session Refresh channel the only issue?