Interesting please put the wall at 10 $
This requires 210 million USD pledged by people using this fund (called "bot" by the OP).
Why should it be written in PHP in the first place? You could write it in any language you can program in... actually few people have a working PHP installation on their home PC, so it might get difficult for them to use.
About this part:
2) It requires people to publicly tell a lot of people how much buying power in fiat they have and pledge to use to back Bitcoin.
False. It requires individuals to tell a server how much they intend to put towards backing the BitCoin, and then to listen to the server's recommendation on a price. Because the bot is open source, different people will likely change the math to alter the level of the backing in their particular pool, or to a level they feel is more correct than the server, be it lower or higher. This organic process helps to set the actual floor.
How is this different from:
Individuals tell a server how much they intend to pay for a Bitcoin, and then listen to the server if there was someone who wanted to sell at this price. Because the server accepts bids + offers, people will likely set their individual prices or - if they think current offers are too high (or low), choose to bid less or more. This organic process helps to establish an actual exchange rate.
?
Anyways, telling a server how much money you want to put towards Bitcoin backing IS making it public, or at least making this sensitive information available to the owner of that server.
What you want to achieve is to have dozens/hundreds/thousands to put a few dollars towards Bitcoin backing and from that to calculate a safe floor.
This won't work as I already said, as this floor is likely far too low to have any effect (would you pay 1000 BTC for a simple book, just because that's the "floor value"?!) - and fractional reserving only works for banks because they control the money, you don't.
In reality your floor might exist but will be irrelevant then (as it is many magnitudes below trade prices) - OR it can crumble, as everyone can remove funds from the floor at will, if the price gets close.
About exploits:
As you control the server (or someone else controls it...) anyone controlling that server can send out bogus data to the owners of this bot.
If I now took control of the server and told it, that there are 210 million USD in reserves in total pledged, the bot would recommend to (or even automatically do) trade BTC at a price of at least 10 USD/peice (maybe even nearly 30 USD/BTC, if you take into account that only ~1/3 has been mined yet). You have a single point of failure in this system and you seem to control it by design. This makes you suspicious, an attack target and a potential scammer.
Also how would you verify the amount of money that people claim to have without actually getting access to it? I might just happen to have a few billion USD sitting on my MtGox account right now...

On a side note:
http://blockexplorer.com/address/19CCVDxm53WZuyGvNr4ZaVFgn1kYha4dC1 shows 0 BTC as of now - do you not even trust your own idea as you don't set a bounty yourself but just want the money of others for that simple idea of yours (called currency backing...)?