While I applaud your willingness to improve your cooker, like forluvofsmoke said, moving your exhaust to the lower side is a really bad idea.
When you say "Dyna Glo vertical smoker", I assume that you mean the DGX780BDC-D 36" vertical and not the 47" vertical offset. The 36" has the firebox directly below the cooking chamber and, to the best of my memory, has an ash tray that a grate sits on and then a firebox with holes in the side all the way around it. above that is a water tray and then 4 racks above that. There is a chimney (exhaust) in the center top of the food chamber and two intake vents at the very bottom on each side of the firebox.
Before we do a test burn to see what we can get out of the cooker for heat, lets pull the door thermometer and run a quick test on it to see how accurate it is. Remove the temp gauge and clean the probe to get any soot or oil off it. Start a pot of water on the stove and bring it to a boil. Once it's boiling, insert the probe into the boiling water (be careful that steam is HOT!). When the needle stabilizes, the temp should read about 212 degrees(#). If it's not, note the temp. For example, if it's reading 232#, then the gauge is 20# high. So you would need to subtract 20# from your reading when you are cooking.
Now that we know what the gauge is really reading, reinstall it in the door using a little hi-temp food grade RTV to seal the hole. If the gauge is way off you may want to replace it with a quality gauge that is adjustable. Just make sure you do the boil test with the new gauge before installing it.
Now lets fire that baby up! Load the charcoal box to 3/4 full. Fill a starter chimney full of charcoal and get it started. While the starter chimney is doing its work, make sure both bottom intake vents and the chimney (exhaust) are wide open. Wrap the water tray in heavy duty aluminum foil but DO NOT add water. We're going to see just how hot the cooker will get. Go get a beer and wait for the starter chimney charcoal to ash over. When all of the coals in the starter are ashed over and burning well, open the firebox door and pour the started charcoal over the top of the charcoal in the firebox (Top down burn method). Careful the starter is hot! double check all the vents are completely open. You can leave the firebox door cracked for the first 5 minutes to assist the fire starting but close it up after that. Go get another beer and pull up a lawn chair and wait (BBQn is hard work!).
After about 20 minutes of waiting and drinking beer you should see the temp in the cook chamber coming up. When the temp gets to 200# (adjusted for the error you have noted above) open the firebox door and throw a few fist sized chunks of your favorite smoking wood onto the coals and close everything back up. after a few minutes you should see smoke starting to come from the chimney. The smoke should ONLY be coming from the chimney. If it's coming from anywhere else, make note of it. You'll need to seal those leaks later with high temp food grade RTV or a hi-temp nomex tape like LavaLock. I prefer using nomex as it's easier to work with.
At this point let the cooker get as hot as it's going to get. With a full firebox and the vents wide open it should get to ~275# or higher. If it doesn't, then you have a serious obstruction in the cooker between the firebox and the cook chamber or a massive air leak and you're going to have to do some sleuthing to find it.
I hope this helps to get the cooker sorted out.
Willie