What is the best way to upload large video files if you have a slow internet connection? Would a satellite phone be a good alternative?

Sanjay is right about the micro SD memory cards. BestBuy regularly has the 32Gb microSDHC on sale for $17.  The good ones--like SanDisk.  You get the tiny chip, the adapter and a plastic case.  I mailed a lot of them, with no problems, but those were domestic trips. I'm not informed about the amount of x-ray inspection done on letters, but I just taped the plastic case inside a sturdy envelope and sent them off, with no loss in quality on the receiving end. If you absolutely, positively have to have the footage immediately, I would use BTSync for individual, one person to another transfers.  Bit Torrent is more reliable than other methods, and if the transfer is just between two people, your speed is limited by the sender's upload speed.  If the connection is lost, a BT file picks up where it left off the last time there was contact.  Upload sites don't usually work that way, plus the other traffic to and from the server affects your speed. BTSync was invented last year at Harvard to provide companies with a way to transfer confidential business files securely. The traffic is encrypted. Otherwise, Rory can have someone going to Harare drop off a letter with the FedEx office there, with several of the memory cards (which were backed up at home first) taped inside the envelope.

If you have a slow connection, you could have the upload interrupted. A satellite phone would be worse. The reason for YouTube is people have short attention spans. Make your video shorter. People watch YouTube videos on mobile devices, so the quality does not have to fill a monitor screen. Make your video shorter. As it happens I just watched instructional videos on YouTube on the benefits of different kinds of software. They were all 3 times too long and had bad audio. Make your video shorter. There is too much stuff  on YouTube. Your job is to differentiate. Make your video shorter and easier to find.

By far the best way to send huge files over slow connections is to reduce the size of the file. People accept that news coverage or actualities will have a lower quality than a 4K movie so it is fine to have reduced resolution/size images quickly and the full resolution later. There are many tools for converting video into other formats and you can find them by googling something like "video conversion tools". The tool I use most is a free utility called IWisoft Video Converter, which will let you change size, resolution, frame rate or anything else. You can preset your preferred settings so that the actual file conversion in the field is more-or-less idiotproof.  You can download it from here: http://iwisoft.com/videoconverter/

Crispify Android app automatically cuts off the slow portions from the video while compressing the file size during the process. It all happens just in a single click! Original video shot from GoPro Crispified Video: http://www.crispify.it/watch?v=52cb55fc43396 55% compression achieved for this video by just automatically cutting off uninteresting portions from the video without losing the video quality. Original file: 2 minutes 18 seconds long with file size 53.8 MB Crispified file: 59 seconds long with file size 24.1 MB Learn more about Crispify! But, currently you cannot expect Crispify to give polished output as required by commercials. It works well for all the normal user generated content.