If we compare this structure to ABoK #1010 (modified with say a yosemite finish or with some other securing lock) - it is my personal view that the tweedledee bowline is more complex to tie (and hence more prone to tying errors and memory retention). Compared also to ABoK #1047 ...(figure 8 loop)
Of course it is ! There are many "lockable" bowlines that are more simple to tie than the Tweedledee. ( See the beautiful Lee s lockable bowline, for example, shown at the attached pictures ). However, the symmetry of the Tweedledee bowline is unique, as far as I know. I have tied, systematically and repeatedly, all the bends I know ( that are, most probably, all the bends that are known ) which are composed of links topologically equivalent to the unknot -the bends that generate post-eye-tiable, 'bowline-like" loops, that can be tied and untied in one stage. There is no safer alternative than the Tweedledee bowline.
We have to recognize that "simplicity" of tying depends upon the experience of the knot tyer and the tying method he uses. The tying method that reproduces what the Teeedledee bowline really is, two interlinked shape "8" knots, as shown in :
http://igkt.net/sm/index.php?topic=3989.msg27204#msg27204 makes tying it really easy to remember, easy to tie, easy to inspect and hard to tie wrongly ! However, I am not saying tthat it is easier to tie than the retraced fig.8 loop - which can be tied blindly, by just retracing the line of a fig. 8 knot. However, the fig.8 loop is not post-eye-tiable, and I was searching for a post-eye-tiable ( = "bowline-like") loop. Also, to my view, the Tweedledee bowline is easier to tie and inspect than most complex double nipping loop bowlines with a "yosemite" finish.
The Teedledee bowline...that I believe it wont take any foothold with climbers or mountaineers any time soon.
I would bet on it !

Climbers are very conservative in the use of heir tools ( as most professionals are ), especially in their knots, perhaps because they need to focus their attention to so many other things... However, that does not makes it less secure. Within the acceptable limits we are accustomed to respect, regarding practical knots, it is the most secure post-eye-tiable double nipping loop / double collar
symmetric eyeknot I know. I underline the "symmetric", because it offers two advantages : It ensures an instant recognition of a mistake during tying ( because even the slightest difference from a correctly tied knot inevitably destroys the expected perfect symmetry, and it can be spotted at once during the inspection of the knot ), AND help a more even distribution of forces within such a lanyard knot ( the standing end and the tail are adjacent and parallel to each other, so the fact that only one of the two segments is loaded does not disturb the distribution of the forces running inside the knot s nub too much).
I am interested in the "Twice untucked tweedledee bowline" - have you got any more (clearer/improved) images of this structure showing front and back?
This is a much simpler structure - and I am keen to assess its security and stability..
Come on, Mark ! As its name and origin tells, it is just the Teedledee bowline, when we pull he tail out of the knot s nub two times, for KnotGod s sake !
I wish to draw your attention to a large family of loops that are both PET and TIB. This is a combination of characteristics that makes hem very versatile, without being very complex. See the
pet Loop, shown at the attached pictures, for example. A well known example ( that was
not known to me, until recently !

) , is the Double Dragon. All those loops are eyeknots based on a crossing knot s nipping structure, which is a very stable configuration : it can easily be incorporated into a knot in a way that will ensure it will not open up, and degenerate into an helix - the common danger of the "common" bowlines ( i.e., the non-"Eskimo"-like ones ).