What are the timing and moves to get past the Mud Men in Dragon's Lair?

I’ve been working on completing the arcade version of Dragon’s Lair in my spare time over the last few weeks and I’m stuck on the Mud Men scene. Despite reading two or three walkthroughs that I’ve found on the internet, I simply can’t get past the second move.

The walkthroughs generally suggest hitting SWORD when the Mud Men first appear and then pressing UP after Dirk sheaths his sword. The idea is that you should start hitting periodic UPs while they chase you to the end of the screen, but only moving once Dirk has a slight pause.

I’ve tried this several times and I simply can’t get the first UP to work. Sword works, it bounces off the men, and then Dirk sheaths his sword. Hitting UP before he puts it away, while he’s putting it away, or after he’s done simply fails and I get pulled into the goop. Apparently the machine I’m playing has the difficulty set to EASY.

Walkthoughs referenced:

http://www.dragons-lair-project.com/games/related/walkthru/lair/easy.asp
http://www.ign.com/wikis/dragons-lair/Walkthrough

Any help on what I’m missing here?