First, re: using a 12v battery backup, yes I have a 5ah one in the SG cabinet. If a reboot is required though, you have to disconnect the battery. What I did was install a DPST switch with one pole for the + battery lead and the other pole for one side of the 16VAC input so that both can be turned off together for a cold reboot.
2nd, as to getting around the limitation on the TC, instead of looking at signals received, you could look at status. IOW, instead of looking at
'IF A-1, A-ON Received'
as a condition, use
'IF A-1 is ON'
as the trigger. At the end of the event you can set A-1 to IDLE if you want to 'reset' the status without turning it off. In fact, I do the 'IDLE' status at the end of each of my Alexa trigger events.
That does have some limitations but in basic applications it'll usually do the job.