Right now I myself don't have a game that is several GiB in size but I'd like to share one way of providing an alternative download option. So here's a simple way you can do large content distribution on itch.io:
1. Archive your product with 7zip. Split it into several files and encrypt with a password. Tick the option to make a self-extracting archive.
2. Put the self-extracting archive ("YourNameHere.exe") as well as a random 5% of the other created files into folder "PAID". Put the rest into folder "DIST".
3. Make an empty text file named "! this is the official distribution torrent, note that some data of the full release is missing here.txt" inside the DIST folder. This will prevent some misunderstandings and help reduce potential annoyed comments.
4. Create a torrent-file of DIST, use a couple of open trackers. Note: You can put an actual demo in the DIST folder to distribute that here as well if you want to. People who has bought the game can just instruct their BitTorrent client to not download the demo.
5. Make the torrent available for free on itch.io by marking it as a "demo". If the torrent does not actually contain a demo make sure to name the file something like "Warning, this is actually not a demo, this is the data distribution for release X.torrent".
6. Archive the PAID folder. Encrypt with the same password as the first step. Tick the option to make a self-extracting archive, but don't split it into several files this time. Name it "run_me_first.exe" or something like that.
7. Make "run_me_first.exe" available for those who have paid on itch.io.
8. Also make a text file named "password.txt" available for those who have paid. Put the encryption password in there, as well as some more detailed instructions on how to use the distribution torrent (you can for example mention that they can delete the files downloaded via BitTorrent after unpacking the game). Even more alternative options for downloads can be put here, FTP servers or links to dedicated web servers that hand out your content.
9. Explain on the itch.io page how this works: They download the main amount of data via BitTorrent. Then place "run_me_first.exe" with the other files and run it. Finally they should run the now-available "YourNameHere.exe". Afterwards the product is ready to be used!
By using this method people only need to download a small percentage of the actual game size from itch.io, the rest comes via BitTorrent and can download at very decent speeds. If there's any pirates around chances are they will help seed the torrent as well, giving paying customers higher speed (note that this method of distribution doesn't increase the piracy threat, they would have pirated it anyway. Now you're at least getting some bandwidth from them).
I hope someone finds this feasible and useful!
Please check out my tools for the Unity Engine at https://winterdust.itch.io/ as well as the game JezzBall Classic.