I also wanted to go to a 4.1 differential. But unfortunately this is not possible with my 4/4 rear axle from 2014, so I was told by Techniques who are very experienced with differentials. A new complete rear axle would be the solution in my case which is much too expensive. But your 2009 model should be no problem to change the ratio.
Since I have about 140 hp I am satisfied with 3.7 ratio. How would it be, Hannes, to keep the diff. ratio but find a good used MX5 gearbox as a first measure? The biggest advantage is that the first two gears are longer than the Ford gearbox and the 5th gear is shorter. This makes the car more drivable, and you can use 1. and 2. very good in case you would also change the ratio.