I might be able to offer a little here, I had a 2 day class sponsered by LeatherMaster. It was all about the process of making leather, the finishing types, and cleaning methods.
Your suit is a pigmented-protected finish. If you can find a Carpet Cleaner Supply, just ask for the 2 part Leather Cleaning system. Part 1 is the cleaner, which is applied to a sponge, lathered up and used directly on the leather to loosen and suspend the soil, dirt, whatever.
Do small sections at a time. After working the cleaner into the leather, and the dirt is now suspended, use a clean terry-cloth towel or wash cloth to wipe up all the moisture.
After working a few small sections, use a hair dryer to dry out all the moisture of the sections you just cleaned. It'll be obvious when it's dry. Repeat as necessary.
Then apply the Conditioner. Small sections, quickly apply it evenly, then kick up the blow drier again and dry it. You want it to dry quickly on the surface, not soak in. That allows the leather to breathe as it should.