Hell just do Dot Torture at 5 yards. Most people can't clean it and it's easier than your drill.
My favorite warm up drill when drilling with my handgun is to begin nearly as close to the target as possible. Focus on putting three shots in same hole. Take large step back, repeat. Step back, repeat, and so forth, striving each time to put the shots in the same hole, until they start to spread out beyond a fist-sized group, then I walk it back in.
From there, my favorite drills are dot torture, followed up by Bill drills.
Quite honestly, I've played around with red dots on handguns and for my purposes, I found it not needed at all. For that matter, I don't much pay attention to the sights at 10-12 yards, but focus on getting the shots into the center mass area as quickly *and accurately* as possible. I don't see a red dot making much difference at those self-defense ranges.
But it is fun using a red dot at longer ranges and I can see in steel plate competition it might be a help.