I disagree with your reasoning.
We are not talking about ownership or rights to numbers, but to the right to get a reward for the time spent and the result with the technology used. if someone has spent time, money to look for the private key, and you want to use this information (because the transfer will reveal the public key, thus you have the possibility of RBF, and you are only waiting for this public key, not looking for the solution to the puzzle itself) then it is not ethical.
It can be compared to cheating on an exam.
This was probably not the intention of this puzzle, however, greed unfortunately often wins - such is the nature of some people. The end of the topic from my side - everyone is the maker of his own fate. It is interesting to see how this community has changed and what weaknesses this puzzle has uncovered.
This is a cracking contest, an arms race of sorts. People attempting to solve this are basically competing with each other to get there first.
While one can work hard, another person can simply work smarter and snag the reward for themselves.
In this scenario one can only "claim ownership" of a coin after it makes it to an address one controls, and not a second before that.
Let's say I have just enough GPU power to solve a key in two years. After running my tools and paying electricity bills for 23 months you go for the same key with enough hardware to crack it in a day.
You say this is fine, but I'll be left in the dust after I spent time, money and effort just like someone who lost to a bot. Why is it so different?
Such is the nature of this challenge. People can outrun each other with better hardware/cracking tools, so why draw this line there now?
A bot is just another tool one can use, it is code just like Keyhunt or Kangaroo.
That said, I think everyone participating in this bot war will just be contributing to turn 6.6 Bitcoins into a transaction fee, it's sad and probably there will be no personal gain for anyone involved.
But I can guarantee you lots of people will be there doing that when the time comes.
In the end it still boils down to "not your keys not your coins" which is a very old saying at this point.