Final position as follows:
The fact that hint 3 moves the king to e3 and not d3 or f3 indicates that this is where he will be mated (the king wasn't blocking the way of other pieces given that he was the first to move and it would be a waste of a move to go to e3 when he could have moved directly to the other spots if he was needed there).
The fact that black had only a single response on his final move indicates that he was in check and was forces to defend his king (too many other valid moves otherwise). This also indicates that the mating black piece did not mate by moving beside the white king (as this would require a protector of that piece, and therefore would give black a second method of capturing the checking white piece).
Because of 2, the mating black piece must be positioned at a queen's or knight's movement away from both kings, and because 1 isolates the kings at e3/e6, the mating black piece must be at g4/g5 or h3/h6.
From here, it's fairly simple to construct the end position in 8 moves:
Given that the white king has three escape routes if he were in check at g3, we use moves 4 and 5 to bring in the queen side knight to block two of them, the white bishop to block the third off via move 6 and we use move 7 and 8 to get the checking/mating queen and knight in position.