How can I reduce moire effects when downsampling halftone comic book images during live zoom on an iPhone or iPad?

I am writing a comic book viewer. It would be nice to provide higher resolution images and allow the user to zoom in while reading the comic book. However, my client is averse to moire effects and will not allow this feature if there are noticeable moire artifacts while zooming, which of course there are.

Modifying the images to be less susceptible to moire would only work if the modifications were not perceptible. Blur was specifically prohibited, as is anything that removes the beloved halftone dots.

The images are black and white halftone and line art. The originals are 600 dpi but what we ship with the application will be half that at best, so probably 2500 pixels or less tall.

So what are my options? If I write a custom downsampling algorithm would it be fast enough for real time on these devices? Are there other tricks I can do? Would it work to just avoid the size ratios that have the most visual moire effects?

As you zoom in an out, there are definitely peaks where the moire effects are worst. Is there a way to calculate what those points are and just zoom to a nearby scale that is not as bad?

Any suggestions are welcome. I have very little experience with image and signal processing, but am enjoying the opportunity to learn. I know nothing of wavelets and acutance and other jargon, so please be verbose.