Gum bichromates appear to have coarse grain, if that's the look you're going for. You can pretty much make the image look anyway you want tonality wise, by multiple printing with different exposure/development times and brush developing. It's best to print with a flat negative though. It's incredibly cheap, fast, and easy compared to carbon printing.
Carbons can handle a very wide range of negatives, by compensating the amount of dichromate used. I've printed with normal in camera negatives, and lith films with a density range of 1.8. It's an incredibly time consuming process, because of the setting up and drying times. It's usually a multiple day thing, so it's very discouraging when things do go well. You'd need access to a completely level surface for laying the glop, and it's a little bit messier process than gum printing, so I wouldn't recommend the process in a household environment. The nice thing about dichromate processes are how cheap they are, and the tonality is dependent on the pigment (usually watercolor) used.
Maybe a salt or albumen process would be an more suitable alternative for you to try, plus you can tone it with your palladium salts if you like the color of the image they give you.