I'm not a huge fan of SAFe, so you may prefer an answer from someone who is. With that caveat out of the way, I believe the foundational error is that your ART Engineer is conflating the Iteration Retrospective (which should be a separate event) with the PI Planning event. Teams should not be doing iteration retrospectives within PI Planning at all.
The only retrospective defined within PI Planning is the Planning Retrospective, which is run by the Value Stream Engineer, not the Scrum Master. Your problem can therefore be resolved by adhering to the framework as defined, rather than rolling additional retrospectives into the wrong event.
PI Planning Shouldn't Include an Iteration Retrospective
PI Planning is similar in intent (if not practice) to Scrum's Sprint Planning meeting. It has a defined agenda, as pictured below.
However, note that the retrospective defined in the agenda is a planning retrospective, not an Iteration Retrospective. There's no Iteration Retrospective in PI Planning at all!
PI Planning Retrospective: The "PI Planning" Definition
According to the framework, the Planning Retrospective is described under PI Planning as follows (emphasis mine):
Planning Retrospective and Moving Forward. Finally, the RTE leads a brief meeting retrospective to capture what went well, what didn’t, and what can be done better next time. Following this, next steps are discussed, including capturing objectives and stories in the Agile project management tools, scheduling upcoming key activities and events … and cleaning up the room!
What isn't made as clear as it should be is that this retrospective is to reflect on the PI Planning event, not on the iteration. As such, it's not a breakout session or a set of concurrent meetings, and doesn't have to be run the same way as an Iteration Retrospective.
PI Planning Retrospective: The "Post-PI Planning" Definition
However, the framework does offer a slightly better definition that is under Pre- and Post-PI Planning. The agenda items are given separate context within Post-PI Planning, which helps to clarify the purpose of the agenda items listed.
Furthermore, the definition of the agenda item here uses the same section heading for the agenda item but also describes who owns the agenda item as the Value Stream Engineer (VSE):
Planning Retrospective and Moving Forward. Finally, the Value Stream Engineer leads a brief meeting retrospective to capture what went well, what didn’t, and what could be done better next time. Following this, next steps are discussed, including capturing objectives, use of project management tooling, and finalizing the schedule of upcoming key activities and events.
Because it provides both context and an owner for the agenda item, this description seems much more clear. However, please note that it also differs from the other definition by giving this job to the Value Stream Engineer (VSE) rather than the Release Train Engineer (RTE). In either case, the agenda item owner is not the Scrum Master, and you are therefore not the one who has to manage the retrospective or juggle the participants.