The new ACF fields won’t save because you’re not triggering the additional form with the ACF fields.
From what I can see you have 2 options:
1) I’m not sure what the enhanced review plugin does, but maybe you can remove it and look to add the functionality another way, therefore, allowing you to add the ACF fields as mentioned above OR
2) You see if the enhanced review plugin has a hook/action on save, therefore, once the review form is triggered, you run a function to get the field data from the ACF fields and use update_field() to insert the data
