That fan sounds big enough. Do you have a vent for your sewer pipe down around your room. Plumbing uses a vent pipe to the roof for flow of the drainage and other things. You could attach into that, but it's probably only going to be a 2" time it gets to the roof which might not be big enough to get rid of all that heat. You could run a A/C or those icebox adapter to the lights, but then you'll need a water source?? Fuck it I would just connect it to the water heater like how you have it in your picture. Your water heater doesn't have a fan on it. It just works by the emission flowing up and out. I would just check it at first all the time to make sure that no air in flowing back to the water heater. If you used the right parts and pieces it should give the water heater vent positive pressure. I really doubt it would blow out the pilot light as its in the bottom of the tank.
Just remember install some Co2 sensor in your bedroom and living space just in case. You can buy these at Home Depot for $35 a piece so I would put 1 in the basement, all bedrooms where people sleep and main living floor.