Thanks for the visuals,
Can you put your hand on the gas valve while this is doing it and tell me if you can feel the valve pulsing in tune with the flames ?
Let me know,
You really need to have the gas pressure checked before the appliance and while its running but its a pretty good bet that this valve has water in it or some other type of debris. I see you do have a drip leg at the furnace in the gas line I would take that apart and see if you get anything out of there as far as crud or if you can see water trails. I think you are going to have to start with replacing the gas valve if you don't have any means of checking the pressures.
The gas smell is probbaly from the vlave also.
To have the valve replaced will probably cost you about 300 dollars.
Shouldn't be, the pressure switch should detect a blockage and kill the gas valve if the vent was blocked, that's why I figure the pressure isn't changing much in the exchanger and whatever it is would have to on the incoming side of the exchanger.