Usually what I do to remove ICs is to just clip them off with some very fine wire clippers...then you can desolder the stubs one at a time (try to leave enough to pull on with tweezers). If the amount of solder is not enough, just add more.
It's even possible to put in a new socket without using a solder sucker. All you have to do is use a pin or a needle to poke a hole in the solder after you've heated the pad. It probably takes a little longer than using the correct tools, but it works okay and doesn't seem to cause any damage.
I'm not sure how well this would work on an odin chip. I have done this to remove SGS Thompson RTCs, but those had pins that were more exposed on the sides like a regular IC. I suppose if there is enough clearance at the bottom you could use some really fine clippers.
Or if you have two 45+ W irons, you can solder each row of pins together on the back of the board, and then heat each side simultaneousy with the who irons and lightly tap the chip out. You might be able to do it with one iron if it's hot enough and you switch between the two rows quickly.
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