Thank you for the reply, Trish!
I tried both of the workarounds you suggested and both methods do work!
That said, the method of replacing all the points features to circles that look like points in Illustrator is a better solution than saving as a gif. I might not be using the correct terminology, but this is how I see the difference: when saved as an EMF, the symbols are saves as shapes, or vectors, rather than an image with transparency, or rasters. This allows for the pattern to be viewed at any scale without degradation. The gif, while mostly transparent, has a bit of gray halo, and is blurry when blown up.
Again, thank you! Looks like I'll be replacing points with circles for the next hour... 🙂
Cheers