2000 Hyundai Elantra strange temperature issues

I have had a 2000 Hyundai Elantra for 4 years now. Since I got it, it appears that it will not keep heat in the winter because the temperature gauge would drop from about half way (if I warmed it up) almost all the way down once I was moving good, especially on the highway. In the summers it would seem normal. Then two summers ago (2012), it began to overheat at the end of the summer. A few months before that I had noticed it started leaking coolant when parked after driving. I stopped it fairly quickly the few times it started to run toward the top of the temperature gauge. I know it actually was overheating because the engine hot and the one time it was during a light rain and some steam formed. For reasons unimportant here, I did not drive it from fall 2012 until recently. I got the oil changed in November 2013 and started it a couple times and drove it a short distance and it sat again. I put water in it earlier this month since I didn't want to waste coolant. I started it and it rose to about half temperature but after 25 minutes it would start to bubble violently in the reservoir so I shut it off despite the fact that the heat had not gone much past half way on the gauge. I took out the thermostat and ran it again and it did the same thing. While the thermostat was out, I put it in water on the stove and verified that it does open once the water starts to get hot but I did not test at what temperature it opens or closes as I did not suspect more complex thermostat issues until later. With the thermostat out, I noticed the larger fan was not coming on. I checked the relay and it's good. I had been jump starting the car and did not realize how very dead the battery actually was (2V immediately after shutting off). I replaced the battery and then I removed the radiator to get to the fan because the bottom fan bolts were rusted badly and I could not get them off. While the radiator was out, I flushed it out with a garden hose and got quite a bit of light brown sludge out. It did not seem too thick; it seemed to be forced out fairly easily by the water. I then tested the fan and turned out it was still working so I looked at the temperature sensor nearest to the front of the car by the water inlet and it was gunked up badly. I sprayed it out with some PB blaster (closest thing) and scraped much of the gunk out then proceeded to put it all back together - fan, radiator, sensor. I looked in the reservoir at that point and it also had light brown sludge in it. At that time, I suspected the possibility of a head gasket leak. I had never seen any white milky substance on the inside of the oil cap (I had checked it a few times in the past also when it was overheating). But because I had been running water in it and I thought maybe the milky substance may be from interaction of the antifreeze with oil, I suspected that it may not happen with water. I also do not see white smoke when I run it and it does not seem like the engine is weak. I figure I had a big performance issue with a 135hp motor, I should definitely notice. Next, I tried a proper antifreeze ratio instead of water. I put some coolant in the reservoir to dilute the sludge - dumb I know - since I already had the whole system apart, why wouldn't I take the extra ten minutes to dump that? I filled it with the car running and the radiator cap off. I did my best to burp the system by running it for 30 minutes continually trying to add more coolant but it did not seem to take as much coolant as I expected. It now runs cool in 70 degree weather. If I drive for a while at 35mph or less without turning on the heat or A/C, I can get the temperature gauge up to about 35% at times but it does fluctuate and if I park and let it run, I can get it to 40%. If I turn on the heat, it drops a little and if I turn on the A/C it usually drops more. My current theory is that the previous owner used an engine block sealant, my thermostat is opening too early, and I had an air bubble in the system before flushing. At this point, I am considering a new thermostat and radiator cap but am really puzzled and would appreciate any input you may have.