Could this work?
No. The paper does not give any solution. It leaves out the most important part of how to choose the group of "trusted" people.
Centralization is always the most efficient system. However, corruption always occur due to human nature. Spreading the authority to a hundreds of people may not solve problem. It is just like politician in communist country always vote the same which is essential put power on the same authority.
The natural incentive for somebody with lots of hashing power is to profit by playing by the rules, NOT to cheat.
And if you assume that your attacker is Rich and Powerful but Economically Irrational, then any alternative system that you propose will almost certainly be at least as vulnerable as Bitcoin. Create a system that requires 500 semi-trusted "mintettes" that all agree on a transaction log and then imagine 251 Special Agents infiltrating and corrupting the organizations that run those mintettes.
Increase the number to 40,000 mintettes to make it harder... and you've just re-invented Bitcoin.
If one day Bitcoin user base grow, the mining must become a very specialized industry and this core group should still consist of more or less 40,000 people. This group owns the equipment as investment and look for profit so we can assume they behavoir economically rational. It is much much better than a small group of hundred people.
However, what we need is competition between all those people but not cooperating between them. The pool mining promote cooperation in which pool are acting like "mintettes" in the paper. There is no real solution yet and will hinder Bitcoin. Other problems in the paper are also real, and neither Bitcoin nor his solution solve them.
What is the most secure system possible ?
So far I have seen two systems:
1. Majority of vote. (suggested alternative coin system).
2. Majority of computational power (bitcoin).
The combined of these two systems as a two phase confirmations might work better. All currency holders vote periodically the "hard" checkpoint. Two phase confirmations may be needed for very large amount transaction for more trust. It is more complex and may have conflicts but it depends on implementation.
There will be other more systems in the future.