Yes I've found myself doing the same a few times, before switching to a marquee/select copy and paste. I don't know whether including some form of moving those tiles across would work or cause complications, I'd expect it'd need to be without any tile indices, e.g. just as the tile graphics which could then be indexed manually in the document if needed, or if it that'd be more annoying if you're going between different projects/levels and you have stamped tiles following you when you didn't want to.
I'll make a note to look into the undo-redo as there are some manual rules set as to what should be included in the undo and redo and what shouldn't, so they may need a tweak. I agree things with the possibility to preview shouldn't be shaded with an overlay too, it's been removed in some places so will have a look around for others it hasn't been yet.
Viewing post in Tessarium v1.5.2 – Typographic fun comments
Awesome! Also, I noticed if you move the tool's window, it maintains that position as long as the app is open. I think it might be desirable to maintain the window position even after quitting and reopening the app. You could have a double click to re-center in case someone wanted it centered again.