Is it possible to publish a paid game with a free trail period like so many plays or so many days. If so is it possible to make that clear when people find the game on Apple or Google?
Historically, I don't think similar business models such as a game with the first few levels free and the rest locked behind an IAP have worked very well. They tend to result in bad reviews, despite that being a totally reasonable business model.
The shareware version has historically worked, however it isn't as effective now. I think you are better off with a free and premium experience than IAP to unlock.