Is there a less pejorative term than "woolgathering" to label purposeful thought that ranges a narrow gamut

If you want a term for the activity/phase¹ of

gather[ing] data or quotes or other bits into a notebook without knowing in advance whether I am going to use that material

you could say you are commonplacing or just keeping a commonplace(-book). From Wikipedia:

Commonplace books (or commonplaces) are a way to compile knowledge, usually by writing information into books. . . . Commonplaces are used by readers, writers, students, and scholars as an aid for remembering useful concepts or facts they have learned. Each commonplace book is unique to its creator's particular interests. . . . Scholars have expanded this usage to include any manuscript that collects material along a common theme by an individual.

While you (and society) have moved on to electronic forms of storage, it sounds like your collections of information and your use of that collection otherwise meet the definition and purposes of a commonplace. Wikipedia specifically notes that commonplaces were often used as

an information management device in which a note-taker stored quotations, observations and definitions. They were even used by influential scientists. Carl Linnaeus, for instance, used commonplacing techniques to invent and arrange the nomenclature of his Systema Naturae (which is the basis for the system used by scientists today). [citation omitted]

As for the verb, Wiktionary¹ defines it as

1. To make a commonplace book.
2. To enter in a commonplace book, or to reduce to general heads.
3. (obsolete) To utter commonplaces; to indulge in platitudes.

Although this term has more than a whiff of the Enlightenment era about it, it is also being used today. Examples of usage include the above cited Wikipedia article:

By the 17th century, commonplacing had become a recognized practice that was formally taught to college students in such institutions as Oxford.

As well as

[C]ommon placing is one method used in education, but first and foremost, it is a personal habit that intelligent, thoughtful people have been doing for hundreds of years.
—Mystie Winckler, "Commonplacing for Moms: 10 Tips to Get Started", Simply Convivial, 2017.

Many other examples in blog articles and Pinterest boards can be found.

A 2015 (scholarly) article directly equates the kind of activities you describe with the older, paper-and-pen(cil) practice:

This paper presents illustrative examples of digital technology that facilitates information sorting and recontextualizing. . . . This way of reusing digital information may be compared to similar analogue information management practices, known as commonplacing, found in early modern Europe.
—Jon Hoem and Ture Schwebs, "Digital commonplacing," First Monday 20, no. 7 (2015). From the Abstract.

And another blog post specifically recommends the tool you mention, Evernote, for creating a commonplace (though this author's use of the word as a mass noun is a bit odd to my ear):

Here is how you can take the basic concepts of commonplace and build them into Evernote.
—Taylor Pipes, "Taking Note: How to Create Commonplace with Evernote", Evernote.com, March 4, 2016

¹_{This answer applies to what is asked in the body of the question, rather than the title of the question.}
²_{The OED has a similar definition, but it is paywalled.}

Your question's title and elaboration describe different activities.

The "purposeful thought" of your question's title can be called ruminating.

ruminate verb 1 Think deeply about something. ‘we sat ruminating on the nature of existence’ - ODO

The gathering of "data or quotes or other bits" is simply called the gathering phase. Here's an example of the term in use (emphasis, mine):

Part of my process of getting ready for a sermon series is to gather all the available resources I can on a particular subject or book of the Bible and see how these resources will serve my preparation time. Most of the time during this gathering phase, I realize that it would be helpful if I order some additional resources to help me with sermon preparation. - Pastor’s Corner