I say weaved valleys are chit. They do nothing more for watertightness that wrapped valleys. They just look awful.
I cannot say, still, if the valley is done correctly. If it isnt leaking, it may be done correctly. If it is leaking, it is not done correctly.
This is a cricket, as it diverts water to exit the roof where they all tie together and make a dead valley, at least would have made a dead valley.
I think if it were my house, and decided I would shingle it:
1. Shingle up to the transition that turns into the valley.
2. Flash the side which consists of a fascia board and counterflash
3. Lay ice shield in full length sheets perpendicular to the main flow of water (which is coming towrd me in the pic you sent), covering the entire cricket, and continuing 2' up the adjoining slopes
4. Carry the low side shingle head up into the cricket area
5. Start your first shingle on the cricket side centered and placed, but no nails in the valley. You can nail this shingle up at the tops on either side.
6. Second course of shingles would be butted in the center of the valley with no nails through the normal nail line....you would want to nail this course with the next course's normal nail pattern.
7. Make the steeper sloped roofs your dubbed sides with the cut.
I would feel better with mod bit in a two layer configuration. your average shingler will not know how to install this properly AND make all transitions purty.