New fiction is always an excellent idea! :-) And something I've always found interesting in Dorothy's illustrated, in-depth, costume-based timeline as well as my little script-based one (thanks for the mention, Cloud!), is the presence of gaps. For example, the 1930s are canonically blank. We have no canon on what Nick was doing between "Father's Day" and "Father Figure," as the whole world fell into war. Another blank decade is c.1790-c.1805, from Nick approaching his worst in "Blood Money" to Nick approaching his best in "If Looks Could Kill." And fifty years blank between "Francesca" and "Blood Money," and fifty between "Last Act and "Undue Process," and almost a century between "Sons of Belial" and "Dying to Know You," which is the pivotal period in which Nick first decided to kill "only the guilty" (per "Love You to Death").
Anyway, wonderful holes to fill with fanfiction!
I think there are three main reasons behind Nick's apparent wanderlust: 1) running away from Lacroix, as in the "Father's Day" flashbacks, 2) running toward a cure, as in the "1966" flashbacks, and 3) the exigencies of vampirism -- not getting caught, not over-hunting, "the Dorian Gray syndrome" -- as in the "Hunters" flashbacks.
That third reason plays into the whole mythology of "moving on" for an FK vampire, which we see not only in Lacroix's constant prodding of Nick, and especially his seasonal attempts to dislodge Nick from Toronto (Lacroix's actions in DK, KI and LK are all attempts to persuade Nick to move on, I think, with different tactics), but also in Aristotle's vocation ("Forward into the Past"), Janette's decision ("The Human Factor"), and, arguably, Vachon. Vachon runs from the Inca, of course, and stops running (at least for a little while) after the Inca is dead, but while he would not be moved by the first two of Nick's motivations, he and his whole crew must be equally affected by the third.
When Nick is near Khartoum (in modern Sudan) in the "Faithful Followers" flashbacks, he is between the European mainland flashbacks of "Jane Doe" and "Baby, Baby." Since he is called to the dig by Thomas, and then would perhaps wish to flee from such a horrific scene, or to take his friend's drained body home to her family, "Faithful Followers" probably supplies enough material in itself to explain that particular set of to-and-fro-ing ... if anyone would like to take it up in a story? Nick's friend Helen Ruskin-Slater, before her death, after her death? Pioneering female archaeologist, probably upper-crust English?
Funny thing, though, that we never really got a "Dorian Gray syndrome" plot, where a normal, mortal human who doesn't know about vampires noticed that Nick isn't aging, forcing him to move on. Or am I forgetting an episode?