Hey Kempachii!
If you're using the Itch Launcher, you can directly download from here instead if you'd like. Download, unzip and run.
Saves will sync over automatically.
Updates/New versions take a tad bit longer to release on Itch. If you'd like to obtain the free version as soon as you can, I'd recommend checking out our Patreon release. It requires a Patreon account (free to create if you don't have one already).
Here's a link to the latest free version:
Saves should syn over from your Itch version too. In the rare case is doesn't.
Go to where AHITR is located on your system. In the "game" folder you'll find "saves" - You can copy or move that folder over to the location, in the same place, if your saves don't sync.
Hope this helps!