You could try copying the file directly to the FileMaker Server machine (e.g. a zipped file) then moving it to the Data/Databases directory and setting any permissions on the file. You can then use the FMS Admin Console to open the file - I've done that in the past when uploading the file using the FMP client didn't work.
Thanks Andrew. I didn't realise that I could do that, but I now see that it's easily done, via a Remote Desktop connection and a DropBox link. Seems much more reliable and quick.