You could use a small amount of superglue under the chip (but that makes removing it rather difficult). Or handsolder two pins on opposite edges to hold it in place. Oh, and make sure that the chip is not rotated 90°/180° when you solder it back in.
If you have flux, apply a generous amount along the solder pads.
EDIT: Please do NOT use that "SMD desoldering" stuff if it feels mushy when you heat it. They did not provide any information about the composition of that alloy, and that is a massive red flag: Indium is rather expensive (you need 20% Indium for an alloy with that melting point), and if they don't provide the exact composition chances are they cheaped out and used normal Wood's metal. And that stuff is extremely nasty (it contains 12% cadmium, an extremely toxic element), the last thing you want to do is inhale the vapors when you heat it.
About that "the chip kept oozing metal" part: Have you by chance soldered it with your SMD alloy? Bad idea, that stuff is only good for desoldering as it will expand when it cools down to room temperature.