Your idea of a strangled butterfly is very interesting. I can envision it as a single structure or a series of trade structures (e.g. move from one construction to the next or as a combination). Hopefully, we can build a discussion here if others are likewise interested.
Being new to Apex strategies, I fall back on equity options experience, and in Charles Cottle’s (complex) book (link below), he describes a similar idea and said others have told him it is perhaps the “ultimate” option structure given its ability to win in many scenarios. The option structure apparently evolved from a common adjustment strategy to a butterfly: usual +1, -2, +1 construction and adjusted as the trade moves above (or below) the defined range you add the call (or put) at the point of the wings (some call this a “slingshot”). As we know, there are times when the moves are so swift it is hard to adjust a butterfly, so the trade can be designed as a “pre-adjusted” butterfly on both sides which would be a +2, -2, +2 which could be called a double slingshot - which effectively is a strangled butterfly. This would be one version of the so called “ultimate” structure. [imo, this can be an effective way to finance expensive strangles esp in high VIX conditions AND it can give a strangle a way to break even or minimally profit when expected large moves fail to occur.]
Now given how you have successfully engineered a much simpler iron butterfly for binaries / box spreads, how would you construct either the sequential placement of the butterfly and strange, or the strangle-butterfly combination? Text reference - [Removed link as see no authorization from author to post his work online for free can buy the book on amazon or kindle though I know you whee not hosting this file just don’t want to promote such links ]. I think the book cover is a double butterfly + Strangle combination but it is not really well described in the book; in fact, the book is challenging, and not one i would recommend, but just providing as a perhaps a description of some related ideas.