I don't know of an FTP client that allows you to remotely edit, but if you host gives you an admin cp, some of them will allow you edit through there. If you have an admin cp through your host, click on one of the files and see if it opens up. If it does you can edit and save it there.

The problem with remote editing is that if you make your changes directly to the file on the server, and don't backup between each save, you don't have a current file to pop back in there if there is a problem, and installing an old backup can create other problems.

Better to keep a working copy, until you know that your mods don't create errors, and then rename your working file to overwrite the backup.

It might take a little longer, but it's better then having to reinstall, if you can't find the problem in your coding.