Which professions have taken the lead both in assisting parties to prepare for an adjudication, and in the role of adjudicators themselves?

There is not a leading profession as such, but each of the institutions has adjudication nomination board associated a support/training programmes for their professionals, there are also independent organisations and the legal profession generally that may be able to assist. It is important to consider the technical issue of each case and decide which institution, association or profession it best placed to support you.