Thank you for the tips, Joy.
I did steam up our bathroom - kept the shower running on hot with the drain plugged, ran the sink water, closed windows and door, etc. It was like a sauna in there. My daughter went in and said, "Wow! It's wet in here! I think the chicks will be fine!" I pulled out a dozen chicks who were mostly dry and left three really wet ones in. Put the dry ones in a little basket (ironically, our egg collection basket), lightly wrapped in a towel, for their trip downstairs to the brooder. Then I opened the Brinsea again, took out the egg shells, and sprayed some hot water from a bottle inside before closing it again. No one tried to jump out. It was probably only open for 30 seconds total.
There were three eggs zipped while I was doing this, but it was getting so crowded that I did it anyway. Every time I'd think we were done zipping for a while, another one would bust out, so I just did it. The three that were zipped all hatched within minutes of me closing the Brinsea back up, so I feel confident that the steamy bathroom method worked just fine for us.
As a side note: after the incubator was closed again, I checked the temperature (probably 3-4 minutes later) and saw that it was up to 104-ish. Probably from the hot water I sprayed in there. So I opened the vent all the way, and it was back down below 100 within a couple of minutes. So watch the temp, if you try this method. I was so afraid that the water would cool down while I sprayed it that perhaps I let the tap water get too hot before filling the bottle.
Now that 12 are in the brooder, I have a total of 10 more in the incubator, and six additional eggs that have not yet hatched. At least three have pipped, so I am hopeful for a great hatch rate. I don't plan to open the brooder again until everyone's out and dry, unless there are some eggs that have no pips and the rest of the chicks seem ready.
There you go - proof that you can hatch 28 chicks in a Brinsea 20. Well, at least 22.We'll see how it goes!