Unable to increase Macintosh HD partition size with data in a subsequent partition

Question

I can't make my main Macintosh HD partition bigger. It's limited by the FAT partition in the middle, which seems to be frozen, I can't move it down to make space for my main partition.

To get some background, I originally had those 2 partitions sharing the space in peace. Then, I created a 3rd partition to experiment with another OS. Once done I deleted that new partition, and boom. It became a no-man's land that neither partition can claim.

I just want to have things back the way there were :(