You're correct in that the raster engraving is what you would need to engrave solid letters (for reference, there is a summary of raster vs. vector engraving on the Capabilities and Limitations page of our Custom Laser Cutting Guide). However, the two-tone material that we stock has an opaque core layer that would not allow you to back-light your letters.
You might be able to find a similar two-tone material with a translucent core color available through Johnson's Plastics that would work as you're describing. You can order the material and have it sent to us for cutting/engraving, or we can special order it for you (a special ordering fee will apply).
If you prefer to use materials that we have in stock, you can still pull this off by using our translucent white acrylic and painting the "background" areas black. If you vector etch the outlines of your letters through the protective masking, you'll be able to peel the masking from the areas you wish to paint, leaving the letters covered during the painting process (like a stencil). The larger the letters are, the easier it is to peel. Small/thin text is still doable, but you'll want to be extra careful when unmasking so that the letters aren't unmasked by mistake. Once the paint dries and you remove the remaining masking, you'll have translucent white letters with a black background.
This painting method will likely be cheaper, since two-tone materials tend to be pretty pricey. If you have any further questions, please do not hesitate to contact us!
P.S. In case this might be of interest to you, we posted a blog article about a laser-cut LED sign project here: https://www.pololu.com/blog/293/hopes-edge-led-banner.