If the flavour is right then don't mess with the recipe. Putting the box over will keep more heat in and will cook your fish. With my Little Chief I used to place the box over the smaoker and even wrap the box in a tarp. And you do get a product that is smoked, cooked and edible. The good think was that the quantity you get out of the little cheif lets you store it in the fridge without without taking up too much room over the two weeks that the smoked fish lasted me.
I now use the Bradley and I find that after 2-hours of keeping the vent minumally open to really soak in the smoke, I open up the vent to push the drying process. With your smoke is moisture which is coming off the fish. You need to keep the vent open to let the moisture out. I'm looking for that rubbery testure that comes from dried not cooked fish.
I'm considering attaching small enclosed squirrel cage type fan to my smoker to move the smoke around inside and accelerate the drying. I'm also going to incorporate a thermocouple and temp controller to ensure the temp doesn't exceed 150 F. Go over that and your cooking fish.
The other thing is to keep a log of the conditions of every smoke job including receipe, smoke/chip flavour, weather conditions, temp, times, weight and thickness of fish pieces, brine time etc. Once you have enough data, graph your results and you'll improving your success. You'll also get find your most efficient smoke time by minimizing the urgency to open the smoker to check the fish.
Experiment and have fun - that what it's all about.