Have you tried the Technical Support forums above these ones?

Reinstalling games doesn't usually touch local settings like HUD Layout and Hotbar files, which may be where the problem is.

You could try navigating to Documents\My Games\Final Fantasy XIV - A Realm Reborn, identify the FFXIV_CHR004000 folder that is for that character, and move it onto the Desktop (don't delete it). That erases all your local character data such as HUD Layout, hotbars, and character macros - but these files may be corrupted from the crash.

If it works, you can gradually copy HUD Layout, hotbars and macros from the Desktop\FFXIV_CHR004000 back into the Final Fantasy XIV - A Realm Reborn\FFXIV_CHR004000 folder one-by-one until the error happens again. When it happens again you know which file, specifically, is corrupted.