You, my friend, need to bite the bullet and buy a Weber Smokey Mountain. You are trying to modify the Brinkman to be the WSM. I have found that there is some engineering that goes into these things. Example...the amount of play between pcs. ...should be tight so that the dampers/vents allow you to control the air and therefore the temps....also the qty. and size of the vents does matter. The WSM does a great job and seems to be what you are seeking given your post.
You are absolutely right about the Brinkman Electric and high temps....it cooks far too hot. I have heard of some guys hooking up a rheostat to the electric element allowing them to dial up or down the amperage...and therefore dial in the correct needed temps. I'm no electrician...but I'm talking about the same type of rheostat that allows you to dim a light. I'd try this before modifying for charcoal...cuz I don't think you will like the result after modifying that tin can with dampers. Charcoal also imo is just better for smoking....no question about it.
If I were you...I'd sell it or junk it....and look for a good used WSM. I have one I'm selling now on Craigslist...used once...with a Tel Tru thermometer...it is great...if only you were in KC. I am ONLY selling cuz I picked up a Big Green Egg. If the WSM doesn't sell for my price...I'll just keep it for when I do a big cook.
Good luck...I hope this was helpful.
I'm sorry guys but I have to disagree with most of this. My first smoker was a Brinkman electric. It is simple, no hassle and easy to use. A butt takes about 10 hours on mine. Ribs take about 5 hours. I don't use wet chips but I set chunks in between the elements. I do have to replace the wood chunks every now and then. I don't keep it smoking the entire smoke and I get plenty of smoke flavor and my meat has a beautiful smoke ring. I've cooked ribs, butts, chickens whole and quartered on it with fantastic results. I got mine at home depot and I can't imagine a better 58 bucks spent. The heating element is suppose to cook at 225 to 250. I've actually never checked my internal temp, but I haven't gotten a bad piece of meat out of it yet.
Update: I cooked my Thanksgiving Turkey on the Brinkman and I did check the internal grate temp. It was sitting right on 250 degrees. A tad hot but like I said, I've had great results with this little cooker.