Is it possible for the front page view to use a different image style for each teaser item?
First, you need to go one level up, don't think about image styles, think about enity view modes. Then you can control which image style is used for each view mode.

The reason for that is that entity output is cached by view mode. You could theoretically alter each entity and switch out the view mode, the data might actually even be available there, but it will fall apart when the same entity is suddenly in a different position but still cached.

You could try to implement preprocess or another views hook to change the view modes programatically in the render array. That will however not be configurable if that is a requirement.

What we build for our project is a views display plugin that allows to not select a single view mode but one for each entity that is being displayed.