Are you positive that timeouts are to blame?
When you say "a script that is capable of uploading smaller sized files", do you mean to say that you tested it on small text files and it worked?
If so, then the problem is probably related to you not binmode()ing your filehandle...
Try doing this:

open (LOCAL, ">$uploadLocation/$schemedName") or dieNicely("Unable to 
+upload: $!");
binmode LOCAL;
# ... rest of your code
[download]

--perlplexer

Update:
And before I forget... make sure you binmode() both filehandles, the one that you opened for writing and the one that you're reading from;i.e., LOCAL and $file. The open() statement for $file is not shown in your code, make sure you call binmode() right after that open()...