So I'm back from there.
Initially, I had booked a car from Mex Rent but canceled it because of the bad reviews. Then I considered Gecko based on the recommendations here and at other sources. Finally, I ended up having rented from Sixt just across the street from the airport based on the combination of their price and user reviews.
I had no problems with that renting.
I drove between Puerto Vallarta (and within the city) and Punta de Mita and visited a lot of places in and between them and it didn't feel like a dangerous place. I truly enjoy being among the locals wherever I travel and having a car gave me that freedom.
So I think it was the right decision to rent a car instead of booking the transfer.
Thanks to everyone who shared their opinions here!