If the relay contacts are sufficiently rated there is no reason why an AC relay can't be used. I am a little suspicious of the relay in the schematic, a nominal rating of 24V id OK, a minimum operating voltage of 18V is reasonable but a drop out voltage of only 2.4V sounds a bit low to me.
I like to experiment with simulations, so here's your schematic. 5k carries sufficient current to provide 24v 8mA. Notice the resistor carries 4W peaks.
Is there a reason you ruled out a capacitive drop, to reduce mains voltage? It's feasible for low power requirements.
EE2-24NU has only 60W/125VA switching power, unlikely sufficient for your application.
Generally, using at DT contact for mains switchover is never safe. The "open" arc won't be extinguished before the new contact closure, causing a short between both power sources. If switching under load, you need separate contactors for both sources with several 10 ms deadtime.