As of version 0.0.45, Sunken Tower supports exporting and importing saves to and from your local storage. See below for details on how this works.

Export:

Step 1: Open the Data menu from the title screen

Step 2: Select the Export Data option

This will save a file to your computer called "stsave" with  a bunch of numbers, which correspond to the date. Your browser might prompt you to grant permission to save the file. Store this file somewhere safe, such as your desktop. You can rename the file if you wish, as long as it remains as a .json. Your save is now safely backed up and ready to be imported!

Import:

Please be aware that importing a save file will permanently overwrite your autosave with the loaded file!

Step 1: Open the Data menu from the title screen

Step 2: Select the Import Data option

Step 3: Select the Choose A File option

Step 4: Load the file you previously exported

Your save file will be loaded and you can pick up where you left off!