From my reading/discussion a “Boettke Austrian” is simply an honest, engaged, curious economist who takes inspiration from Hayek/Mises (& is thus interested in 3 “black boxes” of economics namely: processes of change & adjustment, development & progress, and institutional adaptation & evolution). An inclusive definition focusing on productivity and fruits.
Hard to take issue with this, as it is a positive & “light” definition that does not worry about details and irrelevant arguments (and makes room for different strains - like bakers yeast it is functional, and full of various types of yeast). A good operational definition. However, to me, the distinction between “Austrian” and “Good” economics seems to be near nonexistent, in terms of "products", and is one of chosen community and identification (specifics that lie behind production of a given work). i.e. a paper one would judge to be "good" could be written either by an Austrian or someone else, and while you could perhaps guess correctly much of the time (Mises reference - yes or no? Hayek? Other Austrian signatures?) the distinction could only be truly made by asking the author.
I can see the value, and in particular the motivational and functional value of taking on the Austrian label, so defined. After all, we must all connect with a community in order to challenge and support each others growth, find mentors, inspiration, have a reference group, etc.
I guess the only problem with the label is that it can signal either "Boettke" or "Crackpot" Austrian - but to the extend that a positive, productive, and inspiring message (i.e. Boettke Austrian) is promoted and propagated by Boettke & his academic offspring/friends the crackpot version will become increasingly weakened and Austrian will take on a positive light.
From an outsiders perspective, Boettke & other "positive Austrians" still has work to do on this end, but judging from his work and many of his students (After Arg!) the label may be salvaged. Since community is important, while I see little value in the Austrian label in terms of "products" (good economics is good economics) I see potentially great value in the "label" on a personal level, or rather the community behind the label.