What is the best approach to handle large file uploads in a rails app?
I've dealt with this issue on several sites, using a few of the techniques you've illustrated above and a few that you haven't. The good news is that it is actually pretty realistic to allow massive uploads.
A lot of this depends on what you actually plan to do with the file after you have uploaded it... The more work you have to do on the file, the closer you are going to want it to your server. If you need to do immediate processing on the upload, you probably want to do a pure rails solution. If you don't need to do any processing, or it is not time-critical, you can start to consider "hybrid" solutions...
Believe it or not, I've actually had pretty good luck just using mod_porter. Mod_porter makes apache do a bunch of the work that your app would normally do. It helps not tie up a thread and a bunch of memory during the upload. It results in a file local to your app, for easy processing. If you pay attention to the way you are processing the uploaded files (think streams), you can make the whole process use very little memory, even for what would traditionally be fairly expensive operations. This approach requires very little actual setup to your app to get working, and no real modification to your code, but it does require a particular environment (apache server), as well as the ability to configure it.
I've also had good luck using jQuery-File-Upload, which supports good stuff like chunked and resumable uploads. Without something like mod_porter, this can still tie up an entire thread of execution during upload, but it should be decent on memory, if done right. This also results in a file that is "close" and, as a result, easy to process. This approach will require adjustments to your view layer to implement, and will not work in all browsers.
You mentioned FTP and bittorrent as possible options. These are not as bad of options as you might think, as you can still get the files pretty close to the server. They are not even mutually exclusive, which is nice, because (as you pointed out) they do require an additional client that may or may not be present on the uploading machine. The way this works is, basically, you set up an area for them to dump to that is visible by your app. Then, if you need to do any processing, you run a cron job (or whatever) to monitor that location for uploads and trigger your servers processing method. This does not get you the immediate response the methods above can provide, but you can set the interval to be small enough to get pretty close. The only real advantage to this method is that the protocols used are better suited to transferring large files, the additional client requirement and fragmented process usually outweigh any benefits from that, in my experience.
If you don't need any processing at all, your best bet may be to simply go straight to S3 with them. This solution falls down the second you actually need to do anything with the files other than server them as static assets....
I do not have any experience using the HTML5 FileSystemAPI in a rails app, so I can't speak to that point, although it seems that it would significantly limit the clients you are able to support.
Unfortunately, there is not one real silver bullet - all of these options need to be weighed against your environment in the context of what you are trying to accomplish. You may not be able to configure your web server or permanently write to your local file system, for example. For what it's worth, I think jQuery-File-Upload is probably your best bet in most environments, as it only really requires modification to your application, so you could move an implementation to another environment most easily.
This project is a new protocol over HTTP to support resumable upload for large files. It bypass Rails by providing its own server.
http://tus.io/