Well, this being a discussion forum, some additional thoughts. I think DC is the way to go. I also appreciate the idea that fussing with a dozen plus switches (converting to LED, adding filtering, etc.) can be a hassle. So for the sake of discussion, we can contrive a requirement that the switches themselves are not to be modified.
One tricky part about staying AC is how to sense the momentary solenoid current surge in a timely manner. AC sensors typically average the voltage or current over many 60 Hz line-cycles to get an accurate reading. As you know, a switch solenoid can do its thing in a fraction of a second. So without timely sensing of the solenoid current, the boost circuit could be late to apply the boost, and late to remove the boost. I suppose you can forego averaging and instantaneously apply the boost whenever the current exceeds +2 Amps (some threshold above the peak of the 1 Amp peak steady-state current). Then the trick becomes the circuit that swaps in the boost voltage 60 times a second - probably want to go solid-state vs. a chattering electro-mechanical relay.
Obviously, sensing the solenoid current increase (and decrease) in a DC configuration can be instantaneous - no delay "waiting" for the voltage or current to cycle. Plus, it stands to reason that inserting a DC boost is "easier" if adding to a steady-state DC than to a steady-state AC. Again, while an electro-mechanical relay might be fast enough, it can never be as fast to pick-up and release as a transistor/solid-state switch. And transistors really appreciate working in an all DC environment!
Another idea easier to implement in DC is remote-sensing - a standard power-supply regulation method. Since all your switches apparently see the same voltage drop, you can monitor the voltage way out at a switch and feed back to the control circuit near the transformer. As a sense wire, this would carry negligible current so thin wire is fine. The controller circuit would boost the voltage at the transformer to maintain a constant voltage (e.g., 13V DC) at the switch irrespective of solenoid activity.
A possible gotcha with DC operation is where you are getting the DC in the first place. If deriving from AC accessory voltage thru a bridge-rectifier, this would make the DC- "ground" voltage different from the AC common. This may have implications if using anti-derail operation. Of course you can get inexpensive DC supplies (e.g. a 90 Watt DC-output laptop charger for $10) that would be an isolated source so can share DC "ground" with AC common but does add to the wiring jungle!