How To Handle Power Outages With Remote Macs?
You might want to consider replacing the MBA with a Mac Mini, perhaps a previously owned model from OWC which as some real inexpensive models. Your needs don't seem to require a superlative machine with lots of RAM &amp; etc. The Mini should be able to provide the startup after power failure option because it is a desktop Mac.
For the problem of starting up the iMac in the circumstances you described, you should consider creating a series of Terminal pmset commands which wakes or restarts your Mac with a frequency you find amenable.
This example should attempt to wake from sleep or power on the Mac on an hourly basis every day:
pmset repeat wakeorpoweron MTWRFSU 01:00:00
pmset repeat wakeorpoweron MTWRFSU 02:00:00
pmset repeat wakeorpoweron MTWRFSU 03:00:00
.
.
.
pmset repeat wakeorpoweron MTWRFSU 24:00:00

If the Mac is already up and running, these commands have no effect. A wealth of information is found in man pmset.
The app Power Manager may also be helpful as it provides a GUI method for setting the same commands.
Disclaimer: I have no financial or other ties to the developers of Power Manager, nor in Other World Computing, Inc.