Issac and Ace are the only real innovators we've seen, and Ace strictly within the bounds of his caster class but assisted by Cubbins. Tram is an odd case. He has the informed ability
to innovate non-traditional solutions to problems. Other than that, he is either shown standing stupidly about wondering what is going on, or being a quick thinker who catches on to the very serious implications of a changing situation before others do. Stanley is the only other innovator we've seen, his battle table trimancer link being called the shrewdest move Wanda had ever seen from him.
The problem isn't with a lack of innovation, it's in that the innovations aren't passed along. After Ace is decrypted and dusted, what other dollamancers are going to be concerned with Accessories? What happened to that turnamancer that made the paddleboats and why are those not more commonly used?
Given the raw power of trimancer links, if the innovation of using them were persistent, someone would have found a way to minimize the danger of using one. We have evidence of previous innovations, but no evidence of someone building upon someone else's innovations. Someone made the Staff of Suckage, Duncan's Laurel of Napster, and several other 'artifacts', but nothing gets passed down or built upon.
The closest we get is for a Side to have a particular method of warfare that they prefer. Jetstone prefers Infantry combat, and Ansom was particularly fond of using siege (in addition to the typical Jetstone setup). Apparently if something doesn't directly involve warfare, it's not worth teaching anyone else how to do it.
That may be how Parson will be able to break things enough to end war. Force other sides to be innovative, pass on that innovation, and continue progressing in an effort to stay ahead of the dread Hamster Parson.