SOLVED. It seems MEMU doesn't come rooted by default. Why, I have no idea. As an emulator running on the PC, I can't imagine a good reason why this is not always enabled. For future reference, here is how to root your MEMU and access your FFT saves.
Rooting MEMU
In MEMU's Home screen, go to Tools, then File Manager. Click on the 3 Bars icon in the top left, then click on the gear (settings) icon that appears in the new menu. Go to general settings, then advanced. Click on "Access Mode" and change it to "Root Access Mode" instead of the default setting. Now exit these menus and COMPLETELY CLOSE AND RE-OPEN MEMU.
Finding your saves in MEMU
Now find your FFT save. The directory is /data/data/com.square_enix.android_googleplay.FFT_en2/files/. The file will be named FFTSAVE.BIN and will likely be under 1 MB in size.
Accessing your saves on the PC
You need to move the file somewhere your PC can see it. Select FFTSAVE.BIN by checking the box next to it. Now navigate to a place MEMU has said it will send files to the PC. One such location by default is /storage/emulated/legacy/Pictures/Screenshots. You can also get close to this directory by selecting the sdcard folder instead of storage, but they both lead to the same place. The file does not have to be a PNG, GIF, etc. Now click on the 3 dots in the upper right and select "Paste Selected Item Here". Once this has completed, the file should appear in your PC, and you should be able to modify the file using LIOS editor.
Using your edited save
Navigate to your saves in /data/data/com.square_enix.android_googleplay.FFT_en2/files/ and delete the FFTSAVE.BIN. Copy your edited FFTSAVE.BIN from /storage/emulated/legacy/Pictures/Screenshots (or wherever else you stored it) and place it in /data/data/com.square_enix.android_googleplay.FFT_en2/files. Now it should be modified when you load it in-game.
Rooting MEMU
In MEMU's Home screen, go to Tools, then File Manager. Click on the 3 Bars icon in the top left, then click on the gear (settings) icon that appears in the new menu. Go to general settings, then advanced. Click on "Access Mode" and change it to "Root Access Mode" instead of the default setting. Now exit these menus and COMPLETELY CLOSE AND RE-OPEN MEMU.
Finding your saves in MEMU
Now find your FFT save. The directory is /data/data/com.square_enix.android_googleplay.FFT_en2/files/. The file will be named FFTSAVE.BIN and will likely be under 1 MB in size.
Accessing your saves on the PC
You need to move the file somewhere your PC can see it. Select FFTSAVE.BIN by checking the box next to it. Now navigate to a place MEMU has said it will send files to the PC. One such location by default is /storage/emulated/legacy/Pictures/Screenshots. You can also get close to this directory by selecting the sdcard folder instead of storage, but they both lead to the same place. The file does not have to be a PNG, GIF, etc. Now click on the 3 dots in the upper right and select "Paste Selected Item Here". Once this has completed, the file should appear in your PC, and you should be able to modify the file using LIOS editor.
Using your edited save
Navigate to your saves in /data/data/com.square_enix.android_googleplay.FFT_en2/files/ and delete the FFTSAVE.BIN. Copy your edited FFTSAVE.BIN from /storage/emulated/legacy/Pictures/Screenshots (or wherever else you stored it) and place it in /data/data/com.square_enix.android_googleplay.FFT_en2/files. Now it should be modified when you load it in-game.