Does the wording of the LHP adequately request all that is needed to heal soul fragment issues, simply requesting that the energies causing all soul fragments be transmuted to accomplish a soul retrieval for all parties involved? Or does there need to be mention of cords and thought forms and the interconnections with the participants and akashic records?

Those mechanistic details do not need to be spelled out. The key is energy, energy, energy. If the negative energies involved with the phenomenon are transmuted, that is taken to represent all-inclusive healing, given there are always many crosscurrents, cross connections, and entanglements by cordings, with thought form generation, and the formation of energetic signatures. So rather than having to spell out all those intricacies and the cords flying back and forth being exchanged and giving rise to new ones, as well as the oversight by other levels of the mind that might cord to any discord becoming lodged in the body, for example, simply making a request for all inclusive transmutation of the negative energies will do nicely.