Well, ended up doing it. Not too shabby, for a first timer (never done any polishing work before). I'll explain the steps below with photos. This'll take you a few hours if you do it by hand like me, but probably a fraction of that if you have a proper sanding/polishing wheel to work with.
First I had to cover the thing up with tape to seal off the sides. I used electrical tape and then masking tape over it. I wouldn't recommend this looking back, instead use just electrical tape all around it, wrapping it from the bezels on the top of the screen to the bottom of the computer covering up all the holes and ports. Wrap it tight so no liquids can get in there. If you want, do a double layer just to be safe since some of the chemicals here can be pretty acidic. You really want to take your time for this part to make sure you're not only closing off all points of entry for liquid, but defining the area you want to work with nicely as well. This tape will act as a border that defines the area that gets sanded and polished. Don't be sloppy like I was or you may end up with some jank results.
Once it's securely covered and liquid proofed along the sides and bezels, generously spray some Easy Off oven cleaner on it. Make sure it starts to bubble up all over the surface area. If it looks like you missed a spot put some more on there. Sit and wait ~10 minutes and let it do its thing.
Once you let it sit for a good long while take a roll of paper towels with you, and start scraping away at the finish. it should come off like mud. Once you scrape it all off it should look something like this:
Once you clean it all off with another clean towel do the same thing one more time, just to make sure. I did it 3 times but I think that was overkill, it's never going to be perfect with just this. Once you're satisfied and cleaned it all off, it's time to move onto the fun part--sanding!
I started off with a 400 grit wet or dry sandpaper. I used my fingers to lightly coat the top with some water before sanding. The first layer of sanding might take a while, especially if you're like me and you have a pretty bad scratched and dented lid where it's all uneven. If you have a sanding wheel for this next part, you probably already know how to use it so just go ahead and do that, being careful to not push down on it TOO hard. If you're like me and you need to do it by hand, I did a cross-hatching technique. I went up and down with the sand paper thoroughly both ways, then spun it around 90 degrees and did the same thing. I repeated this until it made a full rotation, then I used some dish detergent and water to clean it off with some paper towels. You might have to do this multiple times with the 400 grit paper. It might look kinda crappy too at this point but don't worry, it'll get better as we go on. (I forgot to take a picture at this point, sorry)
The next step is to do pretty much the same thing with slightly finer paper, I used 600 grit. This is what it looked like when I was done with that. Far from done, but starting to take its form nicely.
After that was 1500 grit paper. It'll be better still at this point but still far from done (I forgot to take a picture here again).
At this point I think you can go one of two ways. If you have the finer grit paper or you have a wheel for it, move onto sandpaper with grit in the 2000s, then maybe finish off with somewhere in the 3000s or 4000s if you'd like. Since I had neither, I moved onto brass wool at this point. I started with coarse brass wool and did the same technique as the sandpaper, with the addition of making circles around the surface as well. By this point it should really start to look like a decent mirror finish.
Unfortunately you can see that I was a jackass and gave too much attention to one spot there. Try to avoid doing that if possible, it messes with the look a bit. If it does happen you might be able to buff it out with polish, but I wasn't really able to with mine. Maybe if I had a proper wheel I could. Anyway, after this I moved onto the fine grit brass wool and did the same thing. At this point it had a pretty good mirror finish, despite my messed up splotch there. Unless you're looking directly at it you really don't see it, especially in well lit areas.
When your sanding is down to the level you want it to be at, it's time for some polish. I used some Brasso with a couple of old socks to put it on there. You really need to take your time to rub it in there to get the full effect, or it'll just end up looking even duller and worse. If you have any blemishes like I did, now's a good time to try and clean those up.
After that, make sure the surface is dry and cleaned up, unwrap your latitude from its tape cocoon, and pray to god it turns on.
Despite my poor taping efforts I have a relatively nice border defined around this thing. It maybe be uneven if you look really closely at it, but I don't really care, it looks good enough. Just make sure you learn from my mistakes if you try this out for yourself and yours will look even better.