My flat lid with the multiple holes is absolutely no problem to damper off. I always have tin foil at hand for wrapping cuts as they come off, or lining the roaster pans I use for carrying stuff back and forth. Just grab a little piece and plug/cover the hole with it. Really quick and easy.
Cap nipples, plug holes, wait a few minutes before opening lid, remove meat and close top and fires out and barrel is cold in just a little while. By waiting a few minutes after closing down before removing meat, I find that I don't get a lot of flare ups and the fire goes out quicker.
Hot Rod Hog Cookers Association, Charter Member, President