MDM, in answer to your questions
1. I am not sure if a filter always solve the problem (due to the intermittent nature). What I have noticed, is that if the problem starts occurring frequently a new filter definitely seems to reduce the frequency. Does it solve the issue... I'm honestly not sure. I do know that the filters I've been pulling out recently didn't seem like they were NEAR needing to be replaced. (2 were so clean my wife put them back with the new filters because she didn't realize they were used) They are cheap filters, but I thought this would mean LESS filtering, and thus MORE cfm through the filters compared to other filter types.
2. I have a Honeywell digital programmable thermostat (actually can be used for a heat pump...which I don't have). While it has MANY features, I only see 4 wires hooked to the terminals in the back, as my setup is pretty simple. When I say I shut the furnace off, I simply go to the thermostat, set it to "off", wait till the blower fan stops blowing, then turn back on. Works like a charm until the next time my issue occurs, which could be days, weeks, months, etc. Could also be the same day (but usually a filter reduces the frequency). I have noticed that when the "issue" occurs, the thermostat always says "heating" or "heating on" so I do not believe it is the thermostat.
3. I totally agree it sounds like it could be a flame sensor issue. I have a metal rod type that detects the flame. Previous owner had a second flame sensor in the documentation with the furnace. Don't know if it was a spare, or one they had removed due to it being bad. I *think* I threw it in last year to see if it made a difference, but didn't notice any so I took it out. (Or maybe I MEANT to try that...) Either way, is there a way to test this item? I have a blowtorch and a multimeter... Alternatively, I can always order a new one, and throw it in for good measure. It should fix it or rule it out. (I figure the total cost of parts for my debugging should still be less than a single repair bill + I learn something). Do the metal rod ones need to be cleaned? (I always assumed cleaning probably is for eyes that "see" the flame) If they do, should I just use some crocus cloth or sandpaper?
Should I assume (for now) that the filters are NOT the issue, but rather a coincidence? Like maybe when I go in to change the filter I am jarring the furnace enough to wiggle the flame sensor's sporadic connection maybe?
My biggest concern is that when it gets colder, this could happen on a long weekend and a pipe could burst. Luckily where I live it's not too cold yet, and we only get pipe bursting weather for short time periods.
P.S. sorry for the slow reply, and thanks very much for the help!