If you come up to them saying "how much would you want" you're less likely to get a response than "we raised $50000, how much more do you want?".
Perhaps, but I still don't think this justifies less stringent management. Besides, you can always open with "I know we can easily get $50000, how much more do you want?"
That would be a lie, I don't know it without more supporting evidence. And even if we can and we know it, they have no reason to believe our optimism.
I believe that projects like this need measurable attainable goals. Currently it's (appologies for paraphrasing) "If we raise lots of money I'm sure wikipedia will accept bitcoins". I'd like it to be "If we raise $100000 wikipedia will agree to accept bitcoin donations for at least 2 years". The key difference is that with the first there's a very real danger that I'm essentially throwing my money into a black hole, which is no good for anyone. The second one alows anyone to judge if the project was run fairly and achieved its goals.
Essentially I'd like to "kickstarterify" the project.
Your money is thrown into a black hole only in one of the following scenarios:
1. Wikimedia will never accept Bitcoin donations.
2. Wikimedia's decision to accept Bitcoin donations will not be influenced by the amount raised,
and you have no interest at all in donating to Wikipedia, just in getting them to accept Bitcoin.
I personally don't think either is likely.
It's very simple to demonstrate the project was run fairly; the requirements are:
1. No funds are spent for a purpose other than those stated
2. When Wikimedia accepts Bitcoin donations, the funds are donated to them.
Will it help if we rephrase it as two separate goals?
1. Get enough funds to credibly approach Wikimedia (tentative target: 200 BTC)
2. Get enough funds to convince Wikimedia (target: Unknown)
You may not yet have enough information to optimally contribute to the 2nd goal, but you can contribute to the 1st, also important, goal.