@prabbit237 suggested an alternative way to set up the ATTiny555 so that it can be used for rapid prototyping, and I've used it to update the whole system and simplify the build process. 

I'm soldering pin headers on the back of the chip, like so:

so I can reprogram the chip as many times as I like!

Now, all the 555-related code is in a single header, making it easy to integrate into whatever project you like. It just needs 2 extra lines of code:

#include "ATTiny555.h"

void setup() {
  AT555_begin();
}

void loop() {
  // your stuff here!
}

And because it uses interrupts, it leaves the loop completely open for you to do whatever you want!

What I find cool about this is that people have actually found potential use cases for this project (Looking at you, @Matthias Urlichs), so I think it's good that all the code is simpler to use.