I've restored several tooled saddles from the 60s and 70s, and have to say I haven't found a better gadget to get tooling completely clean than a super soft children's toothbrush. I use Bickmore's Bick 1 cleaner, get in there with the toothbrush, and rinse with a spray bottle of water as I go. That Bick 1 cleaner really cuts through the sludge of years and years of bar soaps and oil, but you'll need to condition it afterwards. I use Bick 4 conditioner, and then buff it to a shine. It's simple, but the system really works.
Think of dirty saddles like dirty hair - you shampoo, rinse thoroughly, then condition. (You wouldn't leave shampoo in your wet dirty hair, would you?) The problems you see with people using bar/paste saddle soap or glycerine-based sprays is they never remove the dirt, they just get the dirt wet and sticky. That stuff dries, year after year, until you have a gooey crust. That goo loves to take up residence in the tooling.
Unfortunately, I haven't found any shortcuts to cleaning them that gave satisfactory results. This toothbrush/cleaner/spray bottle method is one of those 'do a little at a time' kind of jobs, usually over the course of a few days. It takes me about a week to clean it, let it dry, then go back through and condition it.