Theme Dev: Generate blocks in a section schema's presets dynamically?

I am trying to achieve the following:

1. Create a side-menu by populating a menu item for every section in the home page. Meaning, if a merchant has added a Slideshow section and a Featured Collection section in the home page, then a side-menu will be created containing 2 menu items.

Here’s a visual example:

2. In the Theme Editor, the Side Menu section should be created automatically and it should automatically contain the 2 menu items as two blocks in its presets.

3. The merchant should be able to edit and change the menu item’s text (SECTION 1 and SECTION 2 respectively in the example above)

4. The merchant should be able to add a background image to the menu item if they want.

The end result would look something like the following:

In the example above, the following should happen in the Theme Editor:

1. The Side Menu Section should be automatically created.

2. The Side Menu Section should contain 4 blocks automatically created (Accessories, Featured Product, About Us, Our Philosophy)

3. The merchant should be able to click on one of the blocks and edit its text (ie the Accessories text) and also have the ability to choose a background image for that menu item (ie the socks image in the case of the first menu item).

I managed to build most of that in Dawn but the main problem that I can’t solve is automatically populating the corresponding number of menu items as blocks in the presets of the Side Menu section.

I can hardcode 4 menu item blocks or I can manually add additional blocks from the Theme Editor, but automatically generate the corresponding menu items and have them appear in the Theme Editor for the merchant to edit is something I can’t figure out how to do because I can’t add variables to the schema’s JSON structure.

Can it be done?