carefully designed to make the calculation of the hash quicker than accumulating transactions from the broadcast stream?
The idea of the hash is that sha256(x)->y is a one way function that gives out pretty random results
So if you know y you can't work out x
If you know x you can work out y but it will be a random result
So carefully designing your own x won't help you predict y so you have to use brute force until you come up with the y you are looking for or start experimenting with some of the SAT techniques