The paragraph on page 3, "For a small converter, a small MOSFET switch such as a 2N7000 is used. ..."
It's interesting, subtle; merely change a single digit and it seems current enough (2N7002 is the SOT-23 version, still very much in use for jellybean purposes, alongside BSS138, BSS84 and others). Just as well, it could mean the "original", generic part, and there's not actually anything to read into. But so too, the choice of #26 (and yeah, a possible motivation is to "make do" with it). We can only speculate, short of e-mailing the guy, heh.
I saw the reference to, but didn't look at, the "single bundle" article. I don't have a problem with that, at least from what I gather from its use in the first document. Indeed, I've done that plenty of times myself, and actually I'd recommend you do it as well, if you can. The biggest benefit is: getting excellent transmission line transformer type coupling between windings. Especially so, if you pair primary and secondary wires (as pairs or quads), and then bunch up however many it is you need to wire up in series and parallel, for primary and secondary. The biggest downside is: you have to painstakingly ohm out every single goddamned wire, to make sure you're getting them all properly in series and parallel..! (Even with color coding, you'll only have so many colors to choose from, but for your case, dozens of strands to cover, so...) But yeah, fine for one-offs.
BTW, if you're curious about off-the-shelf possibilities, shop around for inverter transformers. Nothing wrong with using a, say, 240V to 5V, flyback transformer in reverse! Or maybe a forward type would be more suitable (do you really know what inductance you need, as yet?), or multi-secondary so you can wire them for a CT'd primary, etc. They'll likely be bulkier than what you may be looking for, on account of the squarer shapes (mostly ferrite E-core styles), bobbins with rows of pins, and reinforced insulation, and they tend to be expensive (in part just because you're buying tiny quantities through a distributor, prices are kind of irrelevant -- but anyway, the alternative is your labor, potentially a big savings?).
CCFL transformers are also interesting, but probably much too high a ratio for what you want, and they only come in so many sizes. I guess if you wanted to rewind one you could. They tend to have a low profile and high aspect ratio, so might still fit inside your cell-sized enclosure, and I think the power level is about right, give or take size selection that is.
Tim