Manuel,
Nicely explained essay, and perhaps the 'incompleteness' found by others is only as the universe evolution is not yet complete.
Let me run a scenario for you to test with your derivation. If we assume the evolution of the massively complex universe is 'predetermined' as normally understood, then we may still chose one of two options.
1. Only the 'rules' of interactive behaviour down to the smallest scale were predetermined, so no greater knowledge would know in advance what the effects down the line might be.
2. All interactions are known by some greater intelligence in advance, i.e. each scenario has been run before and the result in all cases is known so predetermined.
If the answer is 2. Which is equivalent to a 'tape playing' then there must have been some original case to create the recording on the tape in the first place. If all is predetermined in THAT way, then it would be possible for the intelligence to check ahead on the tape and see what will happen. There must then have been an original "first recording." Which then sets the question; "how do we know we are not that FIRST recording which predetermines all others!? Of course we cannot.
So reverting to option 1. If all interactions are predetermined but the resultant sequences leading to the further interactions not 'pre-set' as above, then we can simply revert to the present universe we understand. I can make any decision I wish right now, and have not done so before, but the rules strictly dictate my options.
There is a 'watershed' between those options. I can see no case not falling onto one or the other. How can something be PRE-determined if it has not been decided in advance exactly what happened in that particular case? But perhaps you have found another alternative I haven't seen which is in neither category.
Best wishes
Peter