I've replaced the High Limit Thermostat a couple times before and it fixes it for a couple years and then stops working again.
Last time I was in there I noticed there was nothing taking up the space near the bottom left where an hole with plastic cover was located. I could reach in the hole but not easily reach the thermostat.
So this time, I decided to avoid working through each piece carefully and just cut open that hole that I mentioned larger (About 15" wide by 10" tall) and then I was able to easily reach in and change this part.
Now if it ever happens again, it will be a quick and easy switch. Just one screw and I am done. WOOT!