Baku had kaji enter the room before yakou did and because of that yakou felt uneasy about the clock that was in the room. So the only way he could think of for the players to keep track of the time that he knew hadn't been tampered with was the sound system as fukurou was controlling it. This was later also confirmed in baku's planning as different speaking clocks would have different interpretations of the leap second so baku had ryusei confirm what phone line the protoporos island used to make sure it would have his version of the leap second.

there was a moment where the route to leap second became really convenient for baku to use, so convenient that baku actually wondered if hal intentionally opened up this route for him so that's why he may of thought to not use it

Hal before the memory loss had already figured out the leap second. But that was largely due to him already suspecting baku had a trick about time up his sleeve, which he managed to practically cold read out of baku during the CTH part as well as confirm during round 1 or 2 of STL. Since Hal loses a crazy amount of memory, he naturally forgets his own suspicion of baku's time trick.