I cut out the rear trunk piece just like you did. Right behind the spot weld flange on the cross member and then seam welded the replacement piece in and ground the welds smooth. There is no overlapping metal in my repair. That car had no sway bar, but I did have to drill out the spot welds for the tow bracket (you can see it in your picture). That was a PITA. The sides of the replacement pieces are flanged upwards, so you can completely remove the old part and tack weld it to the sides/rear of the trunk.
In your case, you could think about leaving the corners in place (just like you have now) and cutting the sides off the replacement metal. It will save you a lot of time, and would be perfectly acceptable if you're ready to butt weld the pieces together.
If you want to replace the whole piece, you can drill out the spot welds for the tow hook, drill out the welds for the sway bar top brace (flat metal pictured), drill/grind the welds for the sway bar bracket, then remove the rest of the trunk metal. Then weld the new trunk in and then weld all of the bits back on to it. If you did this, buying a new sway bar brace (the flat piece) from Engman would be a good idea, because that piece will probably die when you remove it.
Here are a few more pictures of this repair. I don't have as many as I would like, because I did this when I was just getting started and didn't yet know to take tons of pictures.
Note, the first picture isn't the final cut, there is a lot of metal left on the cross brace that was trimmed away.