How big is it now? Because I don't think that you realize how many blocks 2000x2000x3 is (I am assuming that you make it 3 blocks high)
A 200x200x3 darkroom is made by digging away 120 000 blocks, while a 2000x2000x3 darkroom is made by digging away 12 000 000 blocks.
Let's continue with the math for this darkroom.
Let's say that you use a pick that breaks 3 cobblestone per second. You would have to dig for
4 000 000 seconds, or
66 666 minutes, or
1111 hours, or
46 days (No sleep, rest, food, toilet breaks included)
Now, considering that an adult human sleeps around 8 hours per day, these numbers grow immensely.
I will not count with the super breaker, nor will I count the time it takes to repair pickaxes, run, removing dirt, fighting off mobs/torching etc.
If you were to spend 8 hours per day on making this darkroom, it would take you over 4 months to finish it.
Of course, if your darkroom is almost done, none of this applies.
If you still want to do this, I respect your dedication.