Anyone tried creating a custom view for the overall block list property editor? I'm not talking about views for individual blocks, but presenting the entire list of blocks a bit different from what Umbraco does by default. It seems that in order to accomplish this I have to create my own property editor, but copy most of Umbraco's logic for the block list.

Could create a block list property that takes exactly one element (single item mode). Then have that element have one blocklist property.

Yes - with Block Preview package. Here are Block List Blocks inside another Block List for each tab inside a Block Grid