You can always leave the upload screen to cancel out of a failing upload. By all means do so! If you are noticing failed uploads close it out and try again on a different browser or different internet connection.
The files automatically get retried but there is a not a strong track record for it working to well. We use Filestack in our new workflow because we thought it would be more stable but that really hasn't turned out to be the case.
You can also do what you suggested: upload the imagery to Dropbox or GDrive (or one of the other supported cloud data services) which would allow for direct transfer of the data from them to us for processing.