All right, just threw me off a little that you'd consider speculating or backwards decoding as I wouldn't expect them to be easier, or significantly faster (or maybe you consider parity-independence to be speculation? I can see it).
Yes, I meant parity-independence with speculation. Essentially you assume either you are or are not within a string at the start and do your computation based on that assumption, then throw away the result with the unsound assumption. Both assumptions can share most of their computation I believe, so I can understand one might see it from the other perspective where you'd start with calling it parity-independence rather than speculation with shared computation.
But we only have a finite amount of time and tons and tons of work, so no one has gotten around to it yet. At least now we know that it might be worthwhile for >= ~32 core machines. PRs welcome :)