Electric oil heaters have been around for ages. They resemble old fashioned steam radiator units they used to put in all apartment and hotel rooms. They're oil filled and the oil is heated, then they radiate the heat, eliminating any exposed heating element. There's practically no danger of fire...
Go ahead and try it. It sounds like you have a good handle on what to expect from the two older hens, and your chicks seem to have an abundance of self confidence.
The coop scene at night isn't where your integration problems will arise, and if you have plenty of space for the chicks to move...
You're overlooking how to make life simple for yourself and more fulfilling for the chickens. Buy one of those compact resin tool lockers and move all the garden tools into it. Then remove the partition on the 4 x 4 "coop area in the shed and turn the entire shed over to your chickens. You...