Don't forget that questcomp.com has the 53C80 also. I don't know what the pricing on Ebay is looking like, but it's often higher than questcomp.com. Ah, took a look and that $4.20 with free shipping deal looks pretty sweet.
The chip will be the correct size. There was only one PLCC-44 package used for the 53C80.
As far as removing it goes, I have used Chip Quik. It's been almost a decade since I used it, because I don't need it any more.
If you are deciding between buying Chip Quik and a heat gun, I'd get the heat gun.
Chip Quik is an alloy which you melt into existing solder using your soldering pencil. The allow, when mixed with conventional solder, lowers the melting point of the amalgam. This makes it possible to remove moderate sized chips using just a soldering pencil.
Optional step: Remove as much solder as possible from the pins using soldering pencil and braid.
The procedure in brief would be to coat all the pins on the chip to be removed liberally in solder flux. Then run a bead of Chip Quik on all sides of the chip. Then heat each pin/pad individually, to make sure that the Chip Quik has mixed with the solder.
Finally, go around the chip heating each bead of solder/alloy (4 beads in the case of the PLCC-44) in turn. Eventually, you'll get them hot enough that all four will be above the melting point at the same time and the chip will lift off the board. This requires patience. Do not pry the chip up, you'll lift a pad.
If you tried this without Chip Quik, your chances of ever getting the first bead to stay hot enough to release, by the time you get to the last bead, is very low to impossible.
However, if you use a heat gun and just heat the whole chip at once, then there's no need for Chip Quik. I have a Milwaukee brand heat gun with a dial adjustment on the back, which I bought at Home Depot for less than $40. However, they don't sell that model any more. The dial was perfect for this. Most heat guns only have one or two temperature settings.
When using a heat gun to desolder, it is important to mask nearby components. You can literally blow small componetns off the board. I did the first time I tried it. I use modeling clay. Others use aluminum foil. I like clay because it sticks to the board and doesn't blow away, but foil has advantages too.
I find with my heat gun set to 8 (out of 10) it takes about 2 minutes from a cold start to get the typical chip to release from the board. Maybe a little less for something like a PLCC-44, but a little more for some of the through hole chips with 32+ pins.
Once you have the chip removed, remove any remaining solder from the pads with pencil and braid. Clean the board thoroughly. Then tin just one corner pad. Set the chip in place carefully, and melt the tinned pad to settle its pin into place. Thin solder the opposite corner to secure the chip. Then proceed with soldering the rest of the chip. One can often get away with running a bead of solder across each side of the chip, and then coming back through and cleaning the excess solder off with braid. This can be a lot faster, but runs a (small) risk of hidden shorts.