Hello Georgie. 350 is not too hot to smoke unless you are talking 350c.. But THAT is a WHOLE different story and not for now. What we need to do is discover why you can not get temps down in your smoker. NOW! Here I go sticking my foot in mouth again BUT closing down the exhaust stack is NOT a horrible thing. I do it and I know Wade does it. What you MUST NOT do is close it completely. The next problem is just how much SMOKE are you producing from your smoker? What colour is the smoke coming from the smoker? These are things that are experience related. This is not where we should start. These we can discuss much later. You need to be able to control temps in your new smoker.
Here is my thought. IF you tried the minion method and the lower vents were closed and the temp was STILL 350 and "roaring"; you have an air flow problem. So here is what I would suggest: Go buy some cheap charcoal like as in B&Q. Load the basket and fire it up. What you think you might use in 6-8 hours. Light the whole thing. ALL vents WIDE open. NO MEAT USED. Get good white coals going. Now close down the bottom vents, doors and the stack; leave the stack "cracked" about 1/2 open. Either pour a little water on the coals or "spritz" with a spray bottle. BIG WHITE smoke. Now close up except for that small exhaust opening and see where the leaks are. Now if the smoker is "drawing" properly, air would be "sucked" in from the air leaks and then out the fully open exhaust ( fully open in your case ). So the smoker would be "drawing" air like a chimney and causing the coals to burn hotter and faster. So the smoker is sort of working properly but you have no control. If you still don't really see leaks close the exhaust fully. You must remember what you built that smoker from. It looks GREAT but a propane tank is very thin. As you cut that metal it will warp. You may need many more latches to insure a proper seal. What you should see is billowing white smoke out of the 1/2 open exhaust and the heat should start dropping immediately and the coals got out in a short time. If a fire MUST "breath" and "eat". If it can not it will soon die.
These are just my thoughts. Maybe someone will have a better idea. Keep Smokin!
Danny