Yes that would work nicely. You can make the FNames static or otherwise “constructed once” and use them throughout your code base.
I know this is less than UENUM, but digging deep into LookupEnumName and FindEnumIndex for conversion sounds more like modifications to tools/editor than it does to runtime. My json conversions typically go the int32 route, knowing that there are possible compatibility issues there, but going to/from string is alright also if you are ok with the FName conversions.