I think that, honestly, when I have to just process on a problem, not think, not analyse, not find specific words, but just process, I just let the back-brain grind away without concious words or streams to back it up. The only way I can occupy the conscious mind enough, distract it enough to let that back stuff burble is by doing something that occupies it without engaging it deeply.
Letting the emotional, endocrinal, decision making, doing not thinking part of me work without "you shoulds" and other such phrases getting in the way is hard. I can do it while doing tai chi. I often think that old roseries used to be for precisely that purposes. I think my modern equivalent is the solitaire game on the machine. I can play Spider set to Easy or Medium for quite a while as I process and keep out my stupid second guesses quite nicely. And, usually, when I'm done, I pop into an appropriate application and do what has to be done now that it's all structured so nicely in the back of my head. Sometimes it's just to get enough courage to just do and not try.