Convert High Resolution Logo .psd Into Vector Art For Screen Printing On T-Shirt

I've attached a high resolution logo .psd file that needs to be converted into a layered vector illustrator .ai file for screen printing. The shirts will be printed on a medium gray shirt. We will be using three ink colors, Red, Black, and White. All of the grays will have to be half tones. I also attached one of the smaller logos inside of this layout that is already vectorized to help you finish it a little faster. I wouldn't mind having 2 versions, one that is as detailed as possible but still compatible for screen printing and then one that's perhaps less detailed just in case our screen printer needs something a little more simple. Please stay as true to the original as possible but with the least amount of layers as possible. I need this completed in the next 4 hours. If you can send me the .ai file/s when finished, if everything checks out and looks good, I'll release the milestone. Thanks so much for your help!