Reducing the output of a furnace(derating) is dangerous in that if not a high enough temperature inside the heat exchanger is reached then the there will be condensation in the heat exchanger and the flu. The condensation will rust out the heat exchanger and your flu. If your heat exchanger cracks you'll be buying a smaller furnace.
The way to determine the output of your furnace is to clock your gas meter, there are sites on how to watch the dials and depending on the units that your dial displays you could the seconds for a few revolutions and there is a chart that will tell you the rate its burning at. You just need to make sure its the only gas appliance running when you are checking and the water heater is on pilot only and nobody is using the stove, oven, or clothes dryer.
With all that being said, I also have dealt with bad thermostats that seem to want to only less than 5 minutes. I replaced mine with a Hunter, the package it came with specifically said it can be changed between -1f/+1f and -1f/+2f. I like it because now it runs a 10 minute gas cycle every time which I think is long enough to be reasonably efficient but not too long to where I notice the temperature swing. The Honeywell thermostats with the screws on the back are GARBAGE! I was at someones house once and the burner turned on and the furnace turns the blower on at 75 seconds but while the blower was starting up, the Honeywell's anticipater assumed that the demand was met and so the blower kicked on without any gas running. We decided to see what happened if we raised the temperature 5 degrees on the thermostat with the furnace power switch off. The thermostat displayed raised 2 degrees over 10 minutes without the house actually getting warmer. Needless to say that Honeywell crap isn't there. I had a White Rodgers in my house when I moved in, junk too. Get something you can adjust the room temperature for when it cycles on and off.
I don't think you were hitting a limit switch, normally those act like a fuse or circuit breaker, if I pop my limit switch, I'll need to replace it and the only people I know who can buy one is an HVAC tech and they'll check my heat exchanger to be sure I didn't crack it in the process.
Back to your temperature rise, this sounds like you have an inadequate ductwork issue, if there is enough restriction in your ductwork due to bad design and it can't handle the airflow to keep temperature rise down, you either need to have a lower capacity furnace or your ductwork fixed. It could be in the return side or the supply side or a combination of both. An HVAC tech would measure your duct pressure to determine this, if its over 1" water, you need to fix your ducts or have a lower output furnace.
100k 80% furnace is an 80k output furnace. Sounds like an HVAC installer used a terrible rule of thumb for sizing the furnace when it was installed. Where I live, based on the rule of thumb used by tech's here you wouldn't have an 100k furnace unless your house was about 3800 square feet. The problem with those rules of thumb they are using is they figure your house is as leaky as the leakiest house and not insulated well like the houses of the 50's because they don't do a proper heat load calculation, they base it on bad data.
I provided my own personal load test data of thermostat run times in an 8 hour period when the weather was -20f outside, which is the design temp where I live. Even though I'm well under the needs of even the 40k 95% furnace I'd like to have installed, I was still recommended by the tech to put in a 60k 80% furnace to replace my 75k 76% furnace. If a house needs 25-30k of heat at -20f to stay warm and you put a 48k unit in, its still only going to run half the time on the worst day. Needless to say, I'll never talk to that guy again and you shouldn't talk to anyone who won't do a load test if your furnace ever needs to be replaced.
"So does anybody know what happens when the gas pressure is reduced without changing the orifices? I'm thinking this might lead to a rich flame, but I can't really tell due to the inducer blower sucking it all right into the tubes. It's a low-efficiency model (rated 80% AFUE ) but I'd like to tweak it a little to make it more efficient if possible. I notice that the exhaust vent runs pretty hot. I just think that if more of that heat were removed by the heat exchanger, it wouldn't be going out the chimney. Reducing the amount of flame would cause more heat to be removed from the exhaust gasses before they leave the furnace, meaning higher efficiency."
No, this gets discussed on hvac-talk amongst the professionals regarding 2-stage units, the heat exchanger is sized for a certain amount of heat output from the burners, if there is less heat output then the efficient temperature exposure against the heat exchanger isn't met and if the inducer blower doesn't slow down to compensate for the now 'too large' heat exchanger for the burner output, you lose more of your efficiency. For 2-stage units, if the inducer blower doesn't support changing its speed, a lower burner flame will result in reduced efficiency. If you make an 80% efficient furnace into a condensing furnace(which is required to raise the efficiency beyond 80%) you'll need to have a different heat exchanger setup to produce the proper condensing properties and condensate drain lines and PVC piping wouldn't be needed. An 80% furnace isn't designed for it. Get a 90% and be sure to have a variable speed(ECM) motor if/when you replace it. Don't forget to get that heat load test, preferably after you air seal and insulate if you are going to air seal and insulate, which is something you should do if you haven't.
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