How to speed up publishing papers?
If I'm understanding correctly, the problem you're concerned about is what to do when you've just submitted a paper, and now you have a long wait before you can submit the follow-up paper.  Your question then presumes that a good solution to this problem is to try to accelerate the publication process.

I think that is a bad assumption.  There is no reason that you need to be stalled on your forward progress just because a paper is under review.  Here are two good alternatives that work within the system.


You can continue directly building on the same direction.  If you get to a major milestone and are ready to submit a new paper before the previous one is finished reviewing, you can submit a paper citing the one under review as "submitted," and include the draft paper as supplementary review-only information.
Research typically has a lot of "branching path" options getting catalogued in your "future work" sections.  Why not take a secondary path that you've wanted to investigate but isn't in the same exactly line of progression as the paper currently under review?  That will likely lead to its own interesting results that can be published without dependency on the paper currently under review.


It also seems possible to me that this concern may have arisen due to trying to publish too incrementally.  If you cluster your work into larger "publication units" the time lag will likely be less problematic and a smaller number of significant papers is generally better for your career than a bunch of little incremental papers that nobody cares about.