We know that Hal likely established this match to take down BK & Lalo, the greatest threats to his leadership position, but there's still the weird question of why he hasn't restored his memory, it feels like he could easily do so through Midara if he wanted, since Midara is already giving the leeway of hiding his identity.
I think the reason why has to do with a small interaction when he first lost his memory - when Hal was with Nanpou and Touya, Touya clearly realized his memory was wiped, but Nanpou didn't. After learning of Eba's death, Hal could piece together that the past him took measures to make sure he has some sort of replacement for Eba, and that it's only senior referees, his attendants, who know of his condition.
But since the past him didn't reveal it to all the referees, this created a hole in Nanpou (who only happened to be there), allowing him to escape from his attendant. So I think what Hal intends to do, is patch up that hole in the system, and make it so that he won't be able to escape from his attendant by exploiting the very specific situation of 'having a referee who doesn't know about his condition being there at the time of his memory loss'.
But revealing such a condition is very risky, since it could undermine his leadership abilities (what if he loses his memory during a crucial match or time?), which could then cause some referees to leave or even betray the organization. So I think his idea is to prove that his memory condition is not a problem, by disposing of two powerful enemies of Kakerou at once, while carrying the disadvantages of a wiped memory and working alone, and therefore solidify his position as leader. At that point, he could reveal that he did all this with his memory loss (although Touya seems to be revealing it to other referees anyways, probably trying to patch the same security hole as Hal).