I understand the limitations imposed by the new Firefox, and I wish others would understand what they are rating before throwing out 1 star reviews.

I have to however rate it at 1 star. At this point I think you are doing all you can, by moving a tab into a new window. My issue is that your methodology is highly flawed for any reasonable work flow or use case. You should really simplify the operation. Just give the option to tile the first tab as horizontal or vertical. From there you can keep adding them to the screen.
An example.
Tab1->Vertical
[Main][Tab1]
Tab2->Horizontal
[Main][Tab1]
[++Tab2++]
Etc.. Or you could launch the tile by direction.
M(Left)->1 | 1(Up)->2 | M(Up)->3 | 2(Right)->4 = Error = Slot Full
[2][3]
[1][M]
If you can't control where the windows go or move them after launch, then just cut out all this broken stuff and branch 1 window left or right or up or down. I can all but guarantee that the most used feature is moving 1 tab side by side for a comparison. When the new API gets more mature go back and add features, but for now make it work in a logical way.

I think the thing that does it in for me is that I say I want two tiles, and the add-on creates three. Just create 1 new window with the tab I have selected. This lets you control what 2 tabs you want because you can switch around in the main window.