I have rebuilt the intire brake system on our '32 which is if im not mistaken, the same as a '31. If you need hints or tips i sure can give it but it would take all this page has plus some.
Number one for starters, i would suggest getting a manual for the '31 at
www.fillingstation.com Or call the fillingstation and tell them what your looking for which is a repair manual.
Conversion to juice brakes is okay but the truth is that if you have a properly functioning and adjusted manual/mechanical brake system, it is just as safe AS juice brakes.
For tips i would suggest again, getting that manual, inspecting every part of brake linkage and connections of that car, pull the drums, check the brake shoes, check the brake cams in the carrier bushings (they shouldnt wobble but they wont be tight.) Check the front brake cables for frayage, DEFINITLY have the drums turned at a REPUTABLE brake shop or have them ground at a REPUTABLE machine shop, check the front drum bearings for grease, re-install drums, centralize the brake shoes and adjust the brakes.
All of this will be explained in the manual but if you need more detailed info, dont hesitate to post HERE or PM me. One of us will be more than happy to help further. I just gave a ROUGH detail of what to start with.