Someone just asked about this on twitter and it occurs that this would probably be a useful post to share. So here it is.
If you want to run the game through Steam but keep your save games from a non-Steam version (like the Itch beta), you need to copy the save game files found here:
%appdata%\..\LocalLow\Big Robot Ltd\The Signal From Tölva\SavedGames
… to here:
C:\Program Files (x86)\Steam\userdata\<your steam id>\457760\remote\SavedGames
Please note that these will then show up in your saves list, but each game won’t actually be cloud-synced until the game is loaded and resaved. If you play on multiple machines, make sure all your saves are appearing before you start a new game, just in case something gets overwritten.