Feel free to ignore this question if you think it's tangential to your point, but can you elucidate on why competitive prizes are less scammy than the prior examples?
It seems to me like competitive prizes are not scammy because the way they work is well-understood by those involved, whereas bidding fee auctions are generally poorly understood by those involved (or else they'd never make any money).
While in a standard auction you have to pay your bid only if you win, in an all-pay auction you pay whether or not you win. The standard example is a dollar auction where you're selling a dollar. Bidding a penny to get a dollar seems reasonable, but someone else then might bid two cents. The bidding can keep going even past a dollar, and the more people fighting for the dollar the more the person selling it makes. Bidding-fee auctions are similar, where each bid you make costs money. You might remember Swoopo? They used to put up ads like "An iPad just sold for $21.32!" not mentioning that the participants overall had spent more than the retail cost of the iPad on bidding fees. Eventually people caught on and they went bankrupt.
In a less scammy vein, however, this is also how competitive prizes work. In the X-Prize teams spent over $100M in competition for a $10M prize. I can't find an estimate for how much people spent to win the $1M Netflix Prize but when you look at the number of people and number of teams it was probably well above $1M.
Could we use this for charity? Imagine a donor thought two charities were both excellent and had very similar returns, but they knew lots of other people strongly disagreed and preferred one or the other. By offering to donate $X to the charity that received the most in donations, could they move more than $X to the charity of their choice? It might be even better to make the criterion be the most independent donations of at least $Y, because getting more people to donate has value in terms of expected future donations.
(I suggested something similar a few months ago in a comment on my post on donation matching, but hadn't thought about prizes at the time.)