I reached out to some guys on Facebook, and they directed me to this awesome YouTube video which helped a lot. It's not an exact guide for the kind of lights we have, but close enough...
https://www.youtube.com/watch?v=VXFisvd7FrI
I finally had had enough, and I decided to replace them with light fixtures from Costco. Here's what I wound up getting.
I am basically replacing the light on the left with the one on the right:
Here are the instructions I went through to replace them. I'm not an electrician or a handyman, and this job requires neither. The first thing you have to do is... survive :-). You do this by turning off power to the lights. My circuit breaker is in my laundry room, and is the third switch from the top on the left side. The panel when you open it up will have what the switches correspond to. You should verify this by turning on the light (from the lightswitch), then flipping this circuit breaker switch, and verifying your lights are off. Then go back downstairs and try to turn the lights on and off to make double sure, they can't be turned on.
Once you've verified there's no electricity going to the lights, you are ready to start. Start with getting your fingernails around and under the rim of the old light canister and pull it out slowly.
You will notice there are four wires connected to the light. You'll want to cut these wires. Cut them as close to the light fixture as you can (so the wires are as long as possible). You'll notice that there are four wires going to the light (2 red, and 2 black). The light I bought from Costco only has two wires - one black and one white. Just for informational purposes, red corresponds to black (power) and blue corresponds to white (ground). That will be important as you're thinking about connecting the wires.
Next, you'll want to remove the canister. You do this by removing the screws first. There are four small screws that hold the canister in place. You'll need one of these stubby screwdrivers in order to unscrew them given the tight space. After you've taken out all four screws, pull the canister out slowly until it is all the way out. One of the things I did to make this a little bit easier to put back in was to use a sharpie to mark a spot on the canister and on the dry wall so that when I put it back in, I could just line up those marks and push it back in.
If you look inside that hold, you'll see a little metal box. You push up on that tab, and the front panel can be removed.
When you do that, you'll see something like the following. The important wires in here are two sets of red wires, two sets of blue wires, and a set of white wires and a set of black wires. The white wires and black wires are connected to this cool thing where you can connect other wires (important) to them by simply pushing them into one of the available slots in the rectangular piece -- more on this later).
The red and blue wires that go into that box (and into the metal tube) on the left is important. There are two red wires, and two blue wires. You will only need one red wire and one blue wire. Be careful here though, because once you pull those wires through the metal tube, it will be very difficult to get it back. So I found one red wire and one blue wire that I could pull back and forth from the wires in the canister and the wires in the metal box. I verified that those were the wires by pulling a little on them in both directions. Once I found the wires, I cut it at the connect in the metal box. Again, I cut them as close to the twist connectors to make sure I had the most amount of wire to work with. I pulled those wires all the way through, from the canister all the way through the metal box. So, now there were was only one red wire and one blue wire in the canister. I then found the "other" red and blue wires that were going through the metal tube, and cut them again as close to the twist connector as possible. I had to strip off the end of the wires - this is the most "electrician"-y kind of thing I had to do.
After stripping off the ends of the red and blue wires that go all the way through the metal tube, I pushed them into the white rectangular thingy (some pretty technical terms here, eh?). Notice the pairing - the red wire is with the black wires and the blue wire is with the white wires.
I unboxed the replacement light and separated the orange connector. This was pretty straightforward.
Then I shoved my awl (i think a super small screwdriver would work too), into the orange thing on each side and released both wires.
After you do this, you should strip the red and blue wires in the canister and push them into the orange connector. There is a "B" where the black wire (or red) wire should go. The white wire (or blue) wire should go into the other one.
After you've done this, you can connect the two orange parts again, close the metal box again, push the canister back up into the ceiling (align the sharpie marks you made earlier) and screw in the four screws. At this point, you should be good to go. Go turn the power back and and make sure the light can be turned on and off. If your house burns down, I cannot be held liable.
Once you have verified everything is working, you can put the light back into the ceiling by putting the wires inside the guides in the canister and push the light fixture back up.
I was pretty worried when I started this job, but it was way easier than I thought it would be. My only issue now is whether to replace working lights or wait until they burn out. I've got a bit of a hodge podge right now. I've got some LED flush lights, some of these lousy CFL lights, and another CFL light with a white light instead of a yellow light. It's a mess... But after I replace all the CFL lights with LED ones, I will have reached kitchen light Nirvana. It will be awesome!
Patio Lights
It looks like the lights in the patio under the balcony have a different wiring. Here is a picture.
I don't see the standard red and blue wire like I saw earlier. I will investigate and update here.
Upon further investigation, looks like the same thing:
