Nice puzzle! So here's my attempt (I've tried to hide it so everyone else can keep trying independently):
Spoiler:
I think the governor gives away a key bit of information, 'your foreheads with blue and green ink-spots that I see before me' means that both colours are present in the audience.
After this, anyone who saw 0 others with a particular colour could deduce that they must carry that same colour themselves, and could apply to leave.
The next day, if no-one has applied to leave, that means that everyone must see at least 1 other prisoner with each colour; consequently, anyone who sees exactly 1 other with a particular colour could deduce that they must carry that same colour themselves, and could apply to leave.
The next day, if no-one has applied to leave, that means that everyone must see at least 2 other prisoners with each colour; consequently, anyone who sees exactly 2 others with a particular colour could deduce that they must carry that same colour themselves, and could apply to leave.
The nest day, if no-one has applied to leave, that means that everyone must see at least 3 other prisoners with each colour; and so on....
it's kind of like a proof by induction.
Each day the minimum number of individuals who must carry each colour ratchets up by one, until it gets to 44, at which point all of the green ink prisoners will be able to deduce that they carry green and will be able to leave, after which those with blue will too.
I'm a bit worried by that 320 days thing, but I'm guessing it's a red herring...