Half floor pans question

I believe you can get the full pan in on a 2-door car. Yes, you can do a lap weld. Most people do a butt weld by tacking and then doing the full seam, but if you're up close to the door frame itself you wouldn't lose anything by lapwelding, and you could throw some silicone between the pieces before priming to prevent moisture intrusion.
You can see on my small pans we did a lap weld on each of them, cut close, siliconed, and screwed the two overlapping pieces together around the perimeter to hold the piece close together, and then removed a couple screws at a time and tacked through the hole then came along the perimeter and lapwelded.