Have you considered webtorrent or IPFS for distributing the file? Webtorrent in particular looks very easy to setup, and then the most your server would ever have to handle is the equivalent of a single downloader.
That's definitely the more permanent solution for games like this. I was thinking more along the lines of quickly solving the immediate problem so you don't have to spend more money on a different server. I wouldn't be surprised if you could replace the download with a webtorrent in less than an hour of work and be done with it.