Though I did not overwinter any plants this year, I've overwintered all past years that I've grown chiles, and note that I am also in Ohio. I first ordered from Hirts, on Amazon, and the ladybugs did nothing about the aphids. Then I learned that Hirts doesn't have a good rep for ladybugs here at all. I next bought from buglogical.com, and have kept doing so each year because the ladybugs they send decimate the aphids. BOOM - gone. However, you've got a few things to learn. The first thing you want to do upon getting them is give them some water. They'll come in a mesh bag and you can just sprinkle water on it. Put them in the fridge to calm down a bit, then release them into your grow room at night. Ensure there are cotton balls soaked with water around the plants so they can continue to have a water supply. Put fresh water-logged cotton balls out every day. When the aphids are gone, you are going to need to feed them if you can't get them outside. A mix of agave nectar and water soaked into cotton balls does the trick for a while. However, it's unlikely they will survive long after the aphids are gone.
But here's the thing - you have sprayed with insecticidal soap to kill the aphids, and that will also kill the ladybugs. Good thing is insecticidal soap doesn't last really long, but go ahead and hose/spray down with plain water a few times. Usually the effects of the soap will wear off in a couple weeks max. When you release the ladybugs, only do part at a time. You'll find out quickly enough if there's still too much insecticidal soap on the plants. If you release the last ones and still have an aphid problem, make note to yourself to get the ladybugs first in the future.
PS - After recovering from the trip and getting liquid, the ladybugs often want to mate before finding food. Don't worry, they will be hungry within a couple of days.