The CAA guidance on the conversion process has disappeared.
There is clearly no requirement to use a "staff examiner", you can ask to have designated a foreign examiner if you like, assuming they do the briefing. The CAA can always object and designate another one but I don't think they usually do that.
There is a generic requirement in Part FCL for skills tests to be preceded by a recommendation by the organisation that conducted the training but that was written long before the latest amendment to the Aircrew Reg was passed. If no training has taken place does that render that requirement irrelevant? I'm not sure.
To settle this
in the short term I suggest someone rings up Flight Test Bookings and simply asks them what their current understanding of the situation is, it may not reflect what EASA eventually decides is the correct interpretation but it will decide whether the CAA will
currently designate/agree to a designation of an examiner without an ATO.