Okay, I have finally - after a day of beating my head against a brick wall - figured out the problem. I'll post the solution here in case someone else new to Ulead Gif Animator has the same trouble.
Import your transparent gif images into UGA as usual and do your animation. Click the Optimize tab. At the top of the page, youll see a box named "Matte." Next to it is a button - "Transparency." Be sure the Transparency button is pressed. Now check the Matte box. If it's still showing white or any other color (our UGA defaults to white even when the transparency button is pressed), click inside the box. You'll get a drop-down menu. Choose "None." The interior of the box should revert to the checkerboard pattern of z transparent background. No more jaggies!
Thanks for trying to help, Robert.