In my case the passenger was Gold so can't be certain. However, one thing was that once the seat was allocated by the agent, you couldn't change it yourself in MMB. So maybe they do give free seat allocation.
Assistance passengers do get free seat allocation (full details in ba.com/seating under Disability Assistance) but that's a non-negotiated selection, so it may be best to not use that facility. Obviously the risk of that is that if the passenger then chose an unsuitable seat (e.g. exit row) they would have to be moved somewhere else.
I take the point that you would want to turn up early at VIE, but with HBO people whizzing through at 45 minutes to departure, 2.5 hours is still very early. VIE is a big and yet cramped airport, but it is extremely efficient, some MCTs there are below 30 minutes.
The pre-boarding process SOP, I think you were not a long way off that. What should have happened is that the pre-boards should be sent off first, and thus reach the door of the aircraft first. It may be the start of Group 1 will be immediately behind, but they should then wait at the aircraft door until the assistance passengers reach their seats, then Group 1 can board. The problem that can arise is that sometimes Group 1 will overtake the pre-boards and get to the aircraft door first, but that's not the normal situation. It's a difficult one for the gate crew, for longhaul aircraft the planned time from pre-boarding to doors shut can be just 33 minutes as the maximum start point. If there is a 5 minute delay getting going for whatever reason, allowing 3 minutes to cover the distance, and allowing 5 minutes for final reconciliation checks, then you're try to get 210 people on to an aircraft in under 20 minutes.
I think the broader issue is that travelling with assistance generally remains much more difficult for the passengers concerned, in some cases to the point of shoddiness, and LHR is certainly no exception in this space.