Is there a way to influence research in multiple areas of a field?
I think most researchers want to influence and possibly work in different areas, but we can't all be revolutionaries in several fields.
There are two opposing issues that one needs to balance at any stage of academia (or that pesky thing called life):


Doing anything significant usually takes real time and effort
Each individual has limited resources, such as time and effort


As research has progressed over the past centuries  things have gotten more specialized and there indeed has been a necessary tendency for researchers to focus on more and more narrow aspects of science.  However, the branches of science are highly interconnected, and fundamental work in one area often has ramifications in many areas (which the original research may or may not be involved with).  Recently, there has been more emphasis on interdisciplinary research, which it sounds like the kind of thing you are interested in.  So this opportunity is certainly available for researchers who are interested.  

However, interdisciplinary research is easier with certain specialities than others.  (If you run a lab with lots of specialized equipment, you will be limited by the capabilities of the equipment.)  For instance, interdisciplinary work seems to be pretty common with people who do mathematical biology, or more generally applied math/statistics.  They often collaborate with different specialists in different fields/subfields who want to apply mathematical techniques/models to their problems, and in the process learn something about that particular subfield.  My suggestion, if you want to go this direction, is look for an advisor in graduate school who does (and if possible, whose students do) interdisciplinary research that you find exciting.

Another way to influence people in different areas is through teaching, giving lectures and writing textbooks.  Yet another way is by working for a grant agency or as a policy advisor, to help decide what research gets funded.  Working for a scientific publishing company, as you mention, is also a possiblity, but journal editors are professional researchers.  Similarly, university administration is run by professors.  Thus there are many options, but these typically require specialized knowledge, so the preparation is the same as becoming a researcher.