"It comes from diligere, and so calls us to read with rigour and love, interpreting in charity (as Augustine urged); and etymologically it calls up a method of reading as dislegere (dis = away from; legere = to collect, gather, pick; wander through, follow, trace the footsteps; look at, read)"
This sort of etymology is rather misleading, it seems to me: saying dislection comes from diligere poses such questions as how the <s> arose and where the <gere> disappears to. Rather, the two words, noun and verb arose in parallel from the same root. The verb is, by convention, cited in its infinitive form, but the infinitive is not the base of any other word: it is a derived form.
The root is dĭs-lĕg-. This is what both noun and verb were formed from by suffixation in some early stage of Latin. The infinitive was formed with -ĕrĕ (in fact probably -ĕrĭ or -ĕsĭ at this stage, but let's disregard changes that don't contribute to the comparison under discussion). The noun was formed with the usual -tio, -tion- suffix. The voicing assimilation of /gt/ to /kt/ (ct) was no doubt very early, possibly pre-Latin.
In Old Latin /s/ was lost in this position before a sonorant (such as /l/ or /m/), with the previous vowel lengthening in compensation. So dĭslĕg- became dīlĕg-. Often the /s/ was subsequently restored by analogy (e.g. dismiss), which is why we get variation between di- and dis- forms.
In Old Latin the stress was initial. Unstressed vowels mostly became /ĭ/ before one consonant, /ĕ/ before two. Thus the vowel difference between dīlĭg- and dīlĕct-.
Thanks for the elaborated analysis. Looking at the word from the point of view of poiesis (and that's how it is romantically read by Duerden in the quotation below), dislection as opposed to collection goes through things without a centred idea of collecting something ("co-" assumes meaning, theme, idea, or personality as a sort of centre of gravitation), but rather "reading" them "with rigour and love".