How does Eligius pay out directly from the block then if it must receive the block first???
... in pool "mining" there must be an entity to receive the reward, what is not the pool participant. The reward needs to be transmitted (first transaction) to the entity which "solves" the block.[/b] You are failing to understand that the receiver (thus the "solver") it is not the pool participant.
That is not a correct statement. p2pool and eligius are evidence of that.
The pool creates a coinbase entry assigning the block reward to itself.
That is also an incorrect. Note the specific pools I named. If you don't know how they work well thats fine but it might not be a good idea to provide "corrections"
True.
I was not aware that Eligius pool had changed their way to pay the shares. So you are right, my statement was incorrect.
https://en.bitcoin.it/wiki/EligiusWhen a block is found, all miners who have reached the minimum payout threshold (currently about 0.17 BTC) are paid via the Generation transaction.