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Does the bar labeled "One six note phrase" conform to notation standards?
All the examples of triplets that I've seen before have always had the beams break every three notes, similar to the "Manual Beaming" bar (although usually with just a 3 over each triplet as in this question)
Having just a "3" over the six notes seems unusual, but I don't have any notation reference that directly addresses this case.
The one six note phrase is correct, but instead of putting a 3 over the phrase you would put 6 because you are playing 6 notes instead of 8 (just like on a standard triplet you play 3 notes instead of 2).
This site shows a few good examples of grouped 16th note triples in examples 2, 6 - 9 with example 2 shown below.
The idea is you want to keep the standard beaming the same so in 4/4 every count should be group separately and since two sets of sixteenth note triplets make up one beat. Since typically there are 8 sixteenth notes to a quarter note, but you are using 6 in the same space the 6 helps show that the 6 sixteenth notes go where 8 typically go.
Note the distinction between a sextuplet (an irregular grouping of six notes) and the corresponding pair of triplets. At least conceptually these are two different things. But if you could actually hear a difference from a performance is another matter (what you could do is to make small accents on the first, third and fifth notes in the sextuplet and thereby stress a grouping of 3x2 notes instead of 2x3).
Note also that modern music notation software usually are very flexible and that some tuplets that are possible to produce may be more or less confusion to read or perform.
In your three examples the first is unproblematic; the second is confusing, because it looks like a sextuplet but you have a '3' instead of a '6'; the same is also true for the third example (but here you have made clear that the grouping should equal to a pair of triplets).
