I'm puzzled by the notion of a mediator advising/ giving a view that a $5million proposal should be accepted. This puzzlement is for the following reasons:
1. IF, the CEO had not liked the advice, how would the mediator have maintained their claim of impartiality when they had so forcefully expressed their view in favour, presumably, of the other party's offer? It would then become a case of '2 against 1' in favour of the £5million settlement. Impartial?
2. If the CEO wanted an advisor, why did they pay towards a mediator who, I'm assuming was not an 'expert' in the particular type of dispute that they were mediating? And if they were and that was by design, were they there as an expert advisor or a mediator? Why not simply ask an advisor to advise them, why ask a mediator whose area of skill is in mediating and not giving financial advice?
I guess I'm puzzled by the purpose of having a mediator if they are expected to tell parties what they think they should agree to...isn't that more akin to an arbitrator? In which case why not go to arbitration instead?
I'd also like to question in more detail your comparison with psychotherapy. The role of the psychotherapist is long term and with one party while the role of a mediator is short term, 'step in step out' with more than one party, usually two, so the nature of the relationships with clients are very different and the roles of the professionals are very different. The only similarities I can see are the 'people skills' used by both professions but the processes are entirely different and therefore, in my view,not comparable.
Sorry, but just feel quite baffled by what you have said as it seems to me you are proposing that mediators be something other than mediators - when there are plenty of other professionals/ advisors etc. that would fulfill the roles you are wanting the mediators to take. In which case, why seek mediation?