We can use the Clove or Constrictor not as a more complex double nipping turn, but as a more complex double bight component - and tie corresponding bowlines.
It is the adoption of the midspan bend solution suggested by dfred, extended in the case of PET eyeknots. See the midspan case in (1), and the eye-knot case in (2), (3). See also the attached pictures.
The use of the Constrictor instead of the Clove hitch might not be so necessary, indeed, in the case of the midspan bend, as dfred says - but in the case of the eye-knot, it offers a significant advantage we can not ignore : It binds the two collars together ( the “higher” one, around the Standing Part, and the “lower” one, around the eye leg of the Standing Part ), so the whole knot becomes less prone to “open up”. As the nipping turn in this bowline retains this almost vertical orientation, the danger of opening up and degenerating into a open helix is more severs than in most other cases of bowlines, where it is more inclined.
I was curious to see if I could make the double ( = double collar ) bowline, based on a Constrictor double crossed-bight component, to jam, as I have done with the non-reversed Constrictor bowline discussed in this thread. So, I visited my “laboratory”, and I started jumping over the “experimental devise” with my full body weight, twice as many times as I did when I tested the non-reversed Constrictor bowlines. With such moderate to heavy loading of the small rope I used, if the knot was to jam, it would had jammed after fewer jumps, than the 64 that I tried ! 
The strands were flattened at the turns, the knot was compactified to the limit, yet it was so easy to untie by just a light twist of its collars !
The explanation of the difference between the two cases may be simple : In the Constrictor bowline, where the Constrictor is used as a complex double nipping turn, the one end of it would be loaded by 100% of the total load, and the other by 50%. In the case of the bowline where the Constrictor is used as a complex bight component, its two ends are loaded by 50% and 0%, respectably, of the total load. Biiig difference, indeed.
So I conclude that the Double bight component bowline ( double = two Myrtle-like crossed-bight components, the one after the other, tied around the SP and the eye leg of the SP ), is a very secure bowline, very easy to remember how to tie, to actually tie and to inspect, which not only does not jam, but it can also be untied very easily.