I used to use one of those vertical round smokers as well.
Its been quite a few years since I smoked any carp (probably 10 or more) so I don't really remember how long it took. I can tell you my first turkey I cooked for 20 hours on it. It was snowing like crazy and I was making it for Christmas day. Put four posts into the ground and wrapped a tarp around it. Kinda made a little teepee around myself and my cooler, but that's another story...
I personally don't brine my fish when I smoke them. First off, get some hardwood chunks for smoking. A lot of guys I know only use hickory, but I tend to prefer a mix of hickory and apple, bought 50-50. I try to make sure I let them soak overnight in an old bucket so they smoke, not burn. (if you don't have apple chips, soak your hickory in apple juice, it helps.
I am assuming you have the same smoker. deep pan on the bottom, then a rack, set the other pan on that rack, then a final rack with your fish on it?
Here is a link on someone suggesting how to use one of these.
http://bbq.about.com/od/barbecuehelp/f/f060604a.htm
Personally, I do it a little different for the same reason he explains in the article. I don't use the pan in the bottome to actually put coals in it. I use the pan as a catch pan for hot coals. I put the pan all the way at the bottom, and then I put a rack directly on top of it. This is where I put the coals, that way when they become caked, tap the outside and the cake will drop right into the pan below. I then put the next rack right in the middle with the other pan (my first one didn't have a pan so I used a throw away aluminum pan) and fill about half way with whatever liquid you want to smoke with ( I use a combination of water, beer, and apple juice). Lastly put the final rack on top and this is the only rack you should smoke things on. I usually start with about 3 lbs of charcoal off the bat, then add more as needed. I also put a few 2" chunks of hardwood already soaked in once the coals get good and hot.
Like the link tells you, most times those thermometers on there are junk. Take a good one outta your wife's kitchen drawer, once she tastes your smoked fish, she'll forgive ya. Smoking should be done at NO higher than 200 degrees, if its hotter than that, your cooking it. Also, if ya get hot, throw on some sopping wet chunks and if ya get cool, open the door and stir. Refill the center bowl with more liquid any time it starts to run low.
oh yeah, and about that turkey-quarter 2 apples or pears and throw inside the chest cavity so she don't get too dried out. And if you still have problems burning it, throw down some tin foil under the drip pan and poke a few holes in it. This will allow the ambient temperature to rise, but not allow you to be direct heating the bird.
Hope this helps