Are you swinging your sword to help buffer the input, maybe? If I remember correctly, that works on the left side of the screen, but not on the right side (because you can't use your sword too close to that edge of the screen). Screen-scrolling on the right does require a one-frame dpad tap, without using the sword.
(Personally, I'm pretty okay with scrolling on the right, but I still have a hard time getting sword-buffering on the left to work properly for some reason.)
With the release of the new Nintendo "Game & Watch" which includes an official emulation port of the NES and Famicom "The Legend of Zelda" these versions are allowed for speedrunning purposes, because as far as we can tell, they play exactly the same as the NES versions (subject to change if other d