So...someone made a Final Fantasy IV randomizer. It's based off the US "Final Fantasy II" release, so if you want to try it have that ROM handy. The link below will take you to a page where you can generate a randomized ROM. You can actually control the levels of customization. I just chose "Balanced" since I wanted a healthy mix of randomization. It's really best to let the website explain, but...

My party is Yang, Rosa, Kain, Palom, and Cid. I went to the first dungeon just to mess around (also, chest pickups are randomized). Expect to fight Shadow Dragon. Oh wait, bosses are randomized with my settings and Asura is staring me down. All this was accomplished in under an hour.

Have fun!

https://www.ff4-free-enterprise.com/