Thanks, R0J0hound! If you ever need some artwork (icons, objects) or, perhaps, if you accept donations let me know.
I previously put an AJAX object in, BUT didn't add the "on completed" action so it never returned usable results. Now it works! I can actually save and load my arrays and then process them to create objects, which is very cool:
I'll write down the necessary steps "for dummies" (like me) if someone searches for something similar in the future:
In my case the data is an array so saving is easy - just have a "Download as JSON data" action.
Place a FileChooser and AJAX objects in your project. The Filechooser acts like an actual button so place that on the layout. It also has some properties, like are multiple files possible and what filetypes to accept.
In the event sheet:
Add a FileChooser "On Changed" condition of AJAX - Request Url - FileChooser.FileURLAt(0) "LoadFile" <== This is your tag, to know where the file comes from
Add an AJAX "On 'LoadFile' completed" condition with an Array - Load from JSON string - AJAX.LastData
After this add some actions to process your array.
Voila! File saving and loading.
Extra question, if I may - is there a way to replace the ugly Load button with something else? It's an eyesore and it gets shifted around when zooming in and out in the browser. Ideally there would be a way to shift it off-screen and trigger from another sprite button, but I suspect security measures won't let that happen?