>Despite many accomplishments, published papers, and more, I cannot seem to get past the canned hiring process and actually get before a hiring manager.
With a history like that you shouldn't be going through a canned hiring process.
You're doing something wrong.
Talking to former co-workers and moving into positions at companies they've vetted as decent places to work is often a great deal for all parties involved - you get a good job, work with the same excellent people again, and their company gets a known well-performing quantity. That doesn't work as well when you've progressed to leadership roles too far beyond your peers or have other career goals that are too different like making enough to cease working for money at which point you start your own companies. I suspect new peers you'd like to work with again make that a temporary situation but have yet to verify.
Where that's not reasonable as a senior person you should be having casual encounters with technical directors (in big companies only; at small companies you want to go up the food chain to some one more able and willing to speak about the business), VPs of engineering, or CTOs in person (coffee is popular) or on the phone in which both parties get a feel for each other and determine whether a long term relationship is worth pursuing at this time or in the future. A decent linkedin presence should be enough to net this with inbound contacts directly from executives in young companies and from recruiters for larger organizations.
Those recruiters fall into two broad categories - keyword matchers taking a shotgun approach, and more targeted ones that have a better understanding of how things work and what your CV implies. The former usually don't have anything interesting to offer and I don't have much experience dealing with them. The later will make introductions. Some will try to funnel you directly into a hiring process which begins with a technical phone screen, but any place you want to work (executives recognize engineers' importance to the bottom line and consider you worth their time) you can get away with not doing technical interviews on the first date and push for a personal introduction.