It would be possible, yes. you have to edit the Bio Entry Card template in order to do it though. I recommend adding using this method so your changes are update safe.
Using the custom fields, that’s a pretty darned good idea! I know of only one other where they could not save data, same as you. Unfortunately, I am not able to duplicate why this is happening so I can not fix it. If you’d be willing to give me temp admin access, temp FTP access and let me put your site in maintenance mode, I would be more than happy to spend the time trying to figure out and fixed the bug that is preventing this from working for you.
Let me know.