Just found your addon and I've got a few things.

This is how I handle trapezoids:

Note the aligning pixels on the edge:

you can even do:

I'd really like to use your addon but you use the tilemap/spritesheet workflow where I use the repeating texture workflow. aka I use a 16x16px texture per material and apply that to a surface and make it tile by sizing the uv larger then the texture size. (as you can see in the uv edit view)

Would it be possible to add a feature that places all islands on top of each other on the texture? Like this:

What creates the most work for me is blenders unwrap:

As the projection/size and rotation is completely off.

I solve that by aligning the one edge of a none square face to the textures length:

This works fairly well, if there is no edge that is the size of the texture this gets a bit fiddly tho.

The most pixel perfect results I get is to start with a cube and then place the islands. After that then use correct face attributes to reshape the cube into non square faces. If not done like this it becomes a mess and nothing aligns. However this is not that easy to model with.

Maybe some of this process can be applied to your addon.

Start by reviewing the add-on's existing UV-unwrapping workflow and compare it with the repeating-texture workflow described in the issue. The request covers overlapping UV islands, pixel-aligned projection and rotation, and preserving alignment after reshaping faces; no source files or tests are named, so the intended scope and completion criteria need clarification first.