Approach to control 9 model "fog" cannons

Wow...thank you all for the quick and extensive feedback!
I have the mechanical and basic electronics (LEDs, relays, etc) covered, just not at all familiar with boards and programming.
Here's an attached video of the prototype system in operation on a 7 foot long, 1/24 scale brig. The prototype used a compressor to supply air and a custom built, multi-contact rotary switch to trigger the heat, air and flash functions. II miniaturized the air supply, improved the gun design....now I need to get rid of the rotary switch (big, unreliable, hard to optimize timing) and replace it with reliable electronics.