Usage of the word "steward"

It's right there in the definition you quote, entry (2).

"Someone who protects or is responsible for ... etc." - what they are responsible for is 'the reputation and honor of science'

See also stewardship

the responsible overseeing and protection of something considered worth caring for and preserving.

It's common to see steward used in that context: A steward of the land; a steward of health care; a steward of the profession. It's used in the way that "servant" would be used in the selfsame contexts. If you google "a steward of" or "a servant of" you'll find numerous examples.

Speaking as a scientist, I would not use steward in that sense. Carrying out an experiment or project, even one that requires a long period of time, does not constitute stewardship of the entire scientific enterprise. It does constitute dedication and commitment to the scientific method, but these are expected of all scientists. The experiment in question does not differ in kind from any other scientific experiment or project, and yet few would think of calling every scientist a "steward of science" (although in some sense every scientist is).

You could consider the following:

"He stewarded the Mercury Project, which required precise measurements of the motion of mercury over the course of eight consecutive years.

I don't find any support for this usage in dictionary definitions of steward (the ones I've checked) either, but I believe it's idiomatic; it's not an uncommon usage.

ASIDE: The dictionary definitions of steward (the ones I've checked) all refer to stewards as persons; they omit organizations. But isn't it commonplace to see sentences such as the following?

Organization X is committed to environmental stewardship.

According to Wikipedia, "environmental stewardship refers to responsible use and protection of the natural environment through conservation and sustainable practices". Many organizations are committed to this, or to promoting this.