Hmm, I think of the Stout method and pit composting as different things, primarily in the practical sense that one takes place above grade and the other below it, but also in that pit composting is usually more concentrated IME. I usually think of pit composting as a classic technique for the tropics, where you need a lot of concentrated biomass to get any lasting effect rather than simply having your efforts dissipated by the constant, rapid biological activity. I also usually try to add some stable matter to my compost pits (usually biochar or activated charcoal, but pottery shards as in terra preta are also an option) to provide a stable home for the soil biota that is resistant to biological breakdown. We’re in the humid subtropics with about 44 inches of annual rainfall, so we are on the borderline where pit composting can be really helpful but not actually necessary. Cold piles here are not quite as bad as in your region, but they definitely are better for improving the soil underneath them for future plantings than they are for providing much in the way of finished compost.

Persistent herbicides in hay and straw are devestating! Here it’s picloram mostly, but from what I hear they’re all terribly bad and hard to recover from. I’ve heard that fulvic and humid acids can help with remediation, but haven’t experimented with this myself.

My best tip for heating up a reluctant hot compost, inelegant though it may be, is honestly just to pee on it as much as possible.