Huh, maybe I'll try that sometime on a junk board. I can see how re-using the existing solder would help, but won't it be kind of uneven and lumpy, making it very hard to position the new chip so it's leveled and squared?

I once tried soldering a TQFP chip on a virgin board by tinning the pads with a soldering iron, placing the chip on top, and then hitting it with hot air. It didn't work very well, so I've used the drag-solder technique with an iron ever since. Maybe I should try it again?