^Yeah, that is a good idea if you want to swap the chip.
If that doesn't matter, and I were going to glue the chip, I wouldn't do it deadbug. I'd bend the pins out and clip them (or bend them up if you want to use wire wrap) and glue the chip "live bug." There's no reason to read the pinout upside down, in this case.
If the pinout matched, yeah, I'd go dead bug, then it would be easier to route the wires. Stitch up the close row, straight across. Then stitch up the outer row, over the top.