I would start with the thermostat first, if it is indeed running that hot. The fact that you say it was smoking out of the oil fill cap is not good, tho!
You have the right ideas to check, in the right order. Good luck!!

 Did you check the coolant level in the radiator (not the overflow tank)? The smoke in the oil fill could be water vapor , like in headgasket leak. Just a thought, hope its not, hope its condensation.

 Maybe try a radiator pressure tester for leak down. hopefully someplace like autozone will let you borrow one.

Based on the fact that you smelled "burned oil" and saw something visibly venting from the oil cap, I would say that it was overheating and probably reached 230 degrees or more. I would certainly test or change the thermostat first. If you suspect a blockage in the flow, then go ahead with the flush. I would buy or borrow an infared thermometer and "shoot" the thermostat housing and various other locations where coolant flows. This tool will show you where you have a problem if the thermostat does not correct the problem. 

I strongly suggest you get the overheating problem fixed before draining and refilling the system.

Light her back up again and don't forget to feel the upper radiator hose. I assume your coolant level is up to the top of the radiator.

If the hose isn't hot when the gauge says it is, you're not getting any circulation. You may have some sort of an airlock keeping the water away from the water pump. I had this pesky problem with my wife's '86 and filling the system through a heater hose got the block filled, problem went away. The 86 line from the radiator to the water pump takes a twisty path up and over a frame rail which yours likely does not.

If the hose gets good and hot, it might just be the fan clutch. Those things do wear out over 30 years or so. If the fan turns freely by hand while the engine is hot, you have a shot fan clutch.

Don't worry too much, as a BRIEF encounter over 260 probably is OK, but 300 scares even me. Once you get the overheating problem solved, by all means, drain and refill. These things do not like brown water.

Before refilling, flush it real good with fresh water through the heater hose and out the top of the radiator, you'll have to pull the thermostat to flush.

To get all the water out, you should open or remove the drain plugs from either side of the engine block. You won't get a full 50 - 50 antifreeze mix with the block full of water, but that likely doesn't matter a whole lot in FL.

Dave

Those temps are scarry.  Have you checked the oil, is it milky? Pull the plugs to see if any of them are wet.  Unfortunetly small bolck chevy heads are prone to warping and cracking.  Ok if all is ok then buy a cheep mechanical temp gage. Hook it up under the hood, and check your temp with that. If it is normal then its your gage or sending unit that is bad.  Just remember after you run the car and stop, pop the hood and check the mechanical gage fast, because the engine temp will go up after you stop and turn off the engine.  After that follow what the guys have said above.  One last thing your drain pans, once you drain oil into a drain pan it is almost impossible to clean it out completly.  Boy do I hate that, so to get around that I put a plastic trash bag into the pan, drain the oil or antifreeze, pull the bag out cut a small hole into one corner and drain whatever into empty gallon milk jugs.

A word of caution about the drain plug!

Your car will have a "plug", NOT a petcock, to drain the radiator(unless it has been changed somewhere down the line). Do yourself a favor, and don't mess with it! I can almost guarantee it will twist the entire fitting out of the radiator, and then you'll be pulling the rad. to take to the repair shop!
I have learned this on MANY older cars with the plug type drain, including my '74. While it is a big pain to take the lower hose off, it is the best way to drain the rad., along with the "block plugs" on the side of the engine.

There's no problem with draining the water into the pan you use for oil changes. Just clean it after with paper towels. I only have one large drainpan, that works for anything I need it for.

I think if your rad. has a lot of funk in it, it would be a good idea to pull it, and have it professionally cleaned. Then you could flush the engine while the rad. is out.

If the water level in the rad. was 6" down, then it is low. When you start the engine, the level will go down, as the pump pulls the coolant into the engine. You need some free space in the rad., but 6" is excessive. You may have a leak in the hose to the overflow tank. If it has a leak, it will not be able to return the coolant to the rad. when it needs it(after cooling down). Fill the rad. to about an inch below the rim, where the cap goes, and make sure the overflow is filled to the "Full Cold" mark. Try that and see if the overheat is still as bad. Adams' Apple38656.8582060185

Joel --- My 74 has a petcock valve on the bottom, right side of the radiator.  I just drained, flushed and replaced the antifreeze in my system a month ago.  If it was supposed to have a plug, I wonder if the previous owner replaced mine with a petcock or maybe replaced the radiator. 

Larry

Larry, I'd be willin to bet somebody already twisted the orig. plug out, and had it replaced with the petcock, to keep that from happening again!
I thought about doing that when I busted the rad. on my '74, but then, it wouldn't be "original"!
The original set-up was a plug, but a petcock would be the way to go, if you didn't give a hoot about "originality".