Just think of the things they will consider weaknesses. Then come up with counter arguments. Things like:
"While some may consider my status as an early career person to be a negative, I believe that this allows me to have newer knowledge, better focus, and... with all due respect to my colleagues... a lot more energy. "
"You know, in taking advanced coursework in how to manage groups of people from all walks of life, I was exposed to the research that showed that experience doesn't really equate with performance. Now maybe that's not wholly true. And to answer your question about my lack of experience, I'm sure I have things to learn as I go. But I am in a position in my career where I am extremely used to seeking advice when I am out of my depth. Maybe you see that as a strength, maybe you see that as a weakness. I don't know."
Then you know... basic mirroring of their posture. Positively reinforce things that benefit you in the conversation ("that's a really good point"; "I'm glad you asked that"; etc). Don't reinforce things that get you away from your goals. Look up the interviewers. Dress for success. Etc.
Be aware that they might be using you. It's a standard business move to give a job offer to an early career person at a relatively lower rate. And then to use that lower rate as a point of negotiation for the person they really want to hire. "Look Dr. OLDY, we really want to make this happen, but I have a psychologist who is willing to move across the state and take 60% of what you're asking. Meet me in the middle." Then if Dr. OLDY takes it, they rescind the offer.
So... maybe don't shut down your PP quickly. Maybe have an attorney go over the contract.