In order to use a program like FileZilla you'd need to setup an FTP server on one of the machines you're using. From what I can tell, this seems like it would be a bit of a project for you. I recommend you continue using LogMeIn Pro. If that is too slow, you can always use an online storage option so that your dad can upload the file overnight and you can download it overnight as well. Online Storage | Share Files with Shared Folders | Windows Live SkyDrive
The SkyDrive will basically allow your dad to tell his computer that he would like to share certain folders with his skydrive account. This should upload those files/folders to his account. Once they're uploaded, you should be able to log in via sharing and download whatever files he has chosen to share. Note:
This won't increase your bandwidth, in fact it will make it slower since your dad has to upload and then you get to download once he has finished. However, its a bit easier because your dad won't have to upload files each time he places them in the folder, they'll be uploaded automatically and you can likely setup your computer to download those files automatically.