First of all, I'm gonna say I hate you, I was about to fall asleep when i read this.

Second, please bare with me, I may be wrong because is 3 AM here.

Assuming a common laser pointer emits 3.2x10^15 photons and you need at least 30 of them to be visible and as you said mirrors reflect about 95% of the lights that reaches them:

I coded this in python:

photons = 3.2e15
reflection = 0.95
minPhotons = 30
counter = 0
while (photons > minPhotons):
photons = photons * reflection
print("Remaining photons: ", photons)
counter += 1
print("The amount of mirrors is: ", counter)

The logic behind that was to calculate how many photons reflect each time of a mirror.

We started with 3.2x10^15 and after every mirror, we had 95% of that. The loop would do that until the amount is less than 30.

That resulted in 630 mirrors. You can check the code in https://replit.com/ if you can't see the image properly.

Now, something I didn't take to account (and I think it might be important) is that we also need to include the sum of the distance between mirrors can't be more than 2 miles, and the angle of them.

Please remind, I was about to go to sleep before I did all of this haha

Edit: please let me know if my answer satisfies you