You're trying to solve a straightforward engineering problem with an unfit solution to an ill-defined problem. The solution of sybil problem would not solve the case of coordinated attack by multiple nefarious agents. You can also call this meat botnet owned by master-coordinator. The solution would distinguish this from a normal botnet but in the end your service down in the very same manner and clients gave up most of their privacy for nothing.
Imagine instead the following trivial scheme: instead of burning resources the client would pay to be served in reverse order of payment value. Let's say client is willing to pay 1 cent to be served in the next 10 seconds. The attacker would have to pay more as he have to occupy the whole head of this queue all the time to be successful. Let's say server can process 100 rps - now he's making over a dollar per second, which he can use to scale his serving capacity.
Imagine instead the following trivial scheme: instead of burning resources the client would pay to be served in reverse order of payment value. Let's say client is willing to pay 1 cent to be served in the next 10 seconds. The attacker would have to pay more as he have to occupy the whole head of this queue all the time to be successful. Let's say server can process 100 rps - now he's making over a dollar per second, which he can use to scale his serving capacity.