I know you asked for burner cleaning but don't forget the "chimney". Lots of info on burners but you need your model number etc. But not so much info on chimneys. I was surprised how dirty mine was the first time I checked it, 7 years old at the time. Even though you have a frig cover and a screen under the frig cover, stuff still makes it thru. Take cover off and take a look down with flashlight. Odds are chimney might need cleaning also. Leaves and other burnable material are not good mix when you are dealing a flame. Since cleaning the entire burner and chimney on mine, it has fired every time with good clean blue flame.
Combination of wet dry vac, leaf blower, scotch bright pad, flashlight, mirror were my weapons of choice.
After cutting a hole in the screen to get access for your tools, when done I "sewed" a new piece of screen on, for "thread" using very thin stainless steel rod, better known as a bicycle spoke. I went with same size screen instead of fly screen material. Reason was after reading install manual, it seems like some measurements are critical. So I didn't want to mess up any air flow caculations.
At first how leaves and debris make it pass the screen was a mystery to me. IMO the leaves and debris get under cover and then are caught on top of the screen. Then as they decompose or are made smaller by bouncing up and down as your traveling, they are able to fall down into chimney. Then those little loose pieces get caught on the spider webs and ect as they fall down. Just my opinion. Mirror is for also inspecting the tubing, taking a very good look for any wet spots anywhere.