After playing with this for a couple days I can recommend the Transmit 5 ftp client which is available for Mac and Windows. I'm using the Mac version and it's working great with my ATEM Mini Pro ISO. It has one feature that I absolutely love. There's the expected stuff like being able to save connection details, browse the files using a GUI, and copy files via drag & drop. But you can also set a preference so that if you double click a file it will open right up in the appropriate app based on the type of file. Behind the scenes it's making a temporary local copy but to the user it's as simple as double clicking a video file on the ATEM and having it open up in QuickTime for immediate viewing without going through any extra steps of copying files.
For files that you do want to copy to your local drive and keep permanently, the app can also do a sync so that it will make sure you've copied everything off the disk but without wasting any time recopying files that have already been copied over.
The performance has also been excellent, giving me over 100MB/s on ATEM video files via gigabit ethernet.
https://panic.com/transmit/