I noticed that when I set up an image file I'm able to select exFAT. However, after I mount the image file on a RAM disk, when I go to use the RAM disk for the first time Windows 10 asks me to format the disk. exFAT is not listed (on my machine at least), only NTFS, FAT, and FAT32 are listed as options. Am I missing something or doing something wrong?
Most likely that is because you chose "Hard Drive" image type when you were creating the image file. But when you were creating the RAM disk, you left the "Hard Drive Emulation" option unticked. In this case the image will have a partition table on it. But when it is mounted as a standalone drive, Windows will not be able to recognise the file system.
Therefore, you need to choose Volume when creating an image if you want to use it with a RAM disk without Hard Disk emulation.
Likewise, you need to choose Hard Disk when creating an image if you want to use it with a RAM disk with Hard Disk emulation.