Back around 1980, my cousin built me a launch controller for his senior electrical engineering project. Once he got his grade, he gave it to me. It has a couple things that would be cool to integrate into your project in the future.
Adjustable countdown: It uses a dual 8 segment LED which shows the countdown. I am able to set the countdown anywhere between 1 and 99 seconds with a small dip switch (4 position, iirc). I used to have it at 60 seconds, but I now use 30 seconds. That gives me time to put the controller down, position myself, and ready my camera. The ability to choose and set it something other than 10 second countdown would be nice.
Audio for last 10 seconds: Your diagram shows a buzzer. I don't know if it is for continuity or signals the countdown. My controller beeps on each of the last 10 seconds so that I know the launch is imminent.
An option for clusters: My launch relay is at the pad instead of in the controller. This allows high current at the pad and minimal wire between it and the controller. It uses standard 4 conductor telephone extension cable, cheap and flexible. It can fire off big clusters with a little 12v gel cell or power tool battery.
Automatic launch: The last and most important, my controller launches automatically at zero. I can pause or stop the launch at any time easily by pulling the safety key, which is a 1/8" phono plug with streamer (looks like a "remove before flight" tag) or by hitting the start/stop countdown button. This is the best thing in the world for someone who likes to photograph launches, especially when flying alone or in small numbers with recovery team (your kids) downrange, or if everyone wants to video or photograph the launches. It can also be set to launch traditionally by toggling auto/manual, initiating the safety key, and pressing the launch button.
Probably the coolest thing about my controller is that he designed and built it from parts available in the mid 70's at Radio Shack. I think the closest thing I ever saw to what I have was the short lived custom launch systems from
CNA Systems , and those things were very expensive! I think I paid him about $35 for parts, including the project boxes and a cool looking General Electric (probably mil surplus) wet cell 12v battery that had never been activated before I got it. I didn't pay labor because it was a school project that he was going to build anyway.
Even though I have what I think is the coolest retro launch controller on the planet, I plan to build the Arduino at some point when I've caught up other projects.