As I indicated my post, arranging with a Publico driver to take you is an alternative to a taxi, but you won't get to Playa Grande for RD$150 if the publico is serving as a taxi. Just going from Sosua to Cabarete, a short distance, potentially earns the publico driver RD$42. I believe you could get there in a publico which is serving as a taxi for less than the taxi charges, but it is unlikely to be a huge difference. Playa Grande is a long trip from Sosua.
Yes, you could go as passengers in a publico and save money, but I wouldn't recommend it. You would be crowded, take longer to get there, and have to change from a publico to a very crowded guagua before you arrived at Playa Grande.
Arranging with the publico driver to pick you up at a disignated time doesn't mean he will be there at the appointed time--unless he is paid to spend the day with you. Reason is that between when he drops you off and picks you up, he is likely to be running his normal route. That could very likely affect his ability to pick you up at an appointed time.
Renting a car is certainly an option, and the traffic isn't too bad between Sosua and Playa Grande. There will be less what you consder close calls going in that direction than would likely be the case going between Sosua and Puerto Plata.
If it were me, I would use a taxi or arrange with a publico driver to act as a taxi, either staying with you during the day, or rent a car. Taking one taxi to Playa Grande and another to Sosua will be more expensive because both drivers will need to make one leg of the long trip empty.