How do I transfer professional quality videos to clients?

As a professional videographer, I have recently been struggling with technology, a resource usually on my side, to send a client video files. The client asked for the raw footage, so no compression. These are mp4’s from a GoPro ranging in size from 200Mb to 4.21Gb, and mov’s from a Canon 70d up to just over 2Gb. Google Drive would not let him download all the files, saying that the files were too large to compress for download. Hightail.com was unreliable, failing to upload one of the 55 files and therefore sending none of them. The last resort is to send flash memory or a hard drive in the mail. Avoiding snail-mail, what’s the best way to do this?