You've bumped into the greatest problem with raster graphics. It's certainly possible to increase your DPI (I would use Gimp but most image editors will work, open the existing image, then resize it, change the DPI setting to 300 or 600) - the problem is that your image will likely be resized to appear much smaller - roughly 1/3 to 1/6 of the original size (assuming you started with web-standard 72ppi). It's basic math - you increase the pixels per inch while holding the pixel count constant, you decrease the number of inches.
You can resize the image to keep the inches the same, but doing so requires "filling in the gaps" between pixels with some sort of function, which will probably reduce your image quality. That's why most artists start with as high a resolution as they can, and only resize smaller - it's easier for the resize function to throw away information it doesn't need than fill in information it doesn't have.
Depending on how extensive your workflow is, you could start with your original Sketchup export, start with a higher resolution, and retrace all your painting steps. You could also try a different workflow with vector graphics (Illustrator/Inkscape) - because vector graphics can be resized arbitrarily without loss of resolution.
As for a "layered jpeg" - I'm not really sure what the print shop is asking for. JPEG is a lossy compression algorithm that (afaik) doesn't support layering. Photoshop and Gimp native formats do support layering, and that may be what they're after. Hard to say for certain.
Hope that helps a bit.



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