All my best to your dad. Sounds like he's had a great life and career. My father was also a college professor. You made the best choice to move back home and help.
I echo everything in your final paragraph, the terrific advice to others. And don't just listen to your parents' stories. Encourage them. Record them, even if surreptitiously. It will be treasured later. Ask questions. Grandparents also, if you are so fortunate.
I moved away from Las Vegas in 2008 when my mother caught MRSA in a rehab center. She died within weeks. I planned to return full time to Las Vegas but then my dad was diagnosed with pulmonary fibrosis exactly one month after mom died. That condition carries 2-5 years life expectancy and there is no cure. I am so glad I stayed with dad as his caregiver, even if it derailed many of my Las Vegas connections. Dad thanked me profusely for it. We had many great experiences in those 3 years and 9 months, although I wouldn't wish that condition on anyone.
In our family we have a tradition of making a video recording of a person late in life as they describe their experiences. I highly recommend it. The person dresses well and sits in a chair in an easily recognized family setting as questions are asked but mostly the person simply details their life and anything they want to express. With mom unfortunately it was maybe a year late. We still treasure that video but she was on a medication for a condition called tardive dyskinesia so she was tapping her foot incessantly and simply not as sharp as her life norm. With dad he was still in great shape. It was so tragic he caught the pulmonary fibrosis because mentally he never lost anything. I prepared the interview with dad. For some reason he was skeptical I would be fully prepared, that I would know what areas to explore from his younger years. Yes, that stung a little bit. More than a little bit. But everything went great. Dad perked up once he sensed that the conversation was covering all the topics he prioritized, that my sister and I were allowing him to talk while interjecting just enough questions. Dad told me later that the one thing he didn't want was a stupid exploration of, "What's your favorite this, and what's your favorite that."
With dad we have almost 5 hours of that interview tape, plus several hours of audio tapes I made during day to day experiences. For example, if he was arguing with a company on the phone I'd grab the tape recorder and turn it on for the duration. It may have been mostly mundane at the time but years after his death it's priceless to listen to my dad and how he handled something like that. Day to day experiences and not manufactured events. I'm glad I was so secretive and recorded one type of thing after another: Dinner table, driving in the car, watching sporting events together, you name it.