Unfortunately you can’t stop such uploads on a shared account because the server configuration will need to be changed to make this possible which would effect all of their customers on that server.
Your best bet would be a VPS/dedicated server where you’re able to change the server settings.
A VPS/dedicated server will probably allow you to set the parameters but I think the more cost effective option would to set up an uploader script instead of giving full FTP access.
With a simple upload script you can set the file size limits, the types of files they can upload, and when they can upload.
It is a much more control option and probably will cost you less. And since you are using a Linux based server host, PHP upload scripts are quite prevalent. Just google and you’ll find what you need.