Insulating a 4" gap between roof and false ceiling
First, keep in mind that that venting in the roof rafters is essential to the ventilation of your roof.   Essential.    Do not fill that gap completely, you will be looking at future problems.

If the current gap is 3-4", the most you could do is insert 1.5" max of insulation.  Panels of Polystyrene come to mind because their R-value is better per inch of thickness than roxul/pink stuff.   You will, however, have to follow-up with "Great Stuff" foam to ensure filled gaps if you go that direction.