You're are correct that clause 3.8.3.1 says the weld and HAZ must be "completely" within the bent portion of the specimen after bending. You need to continue to the next clause, 3.8.3.2, and read that "the convex surface of the bend specimen shall be visually examined for surface discontinuities." The convex surface includes the weld, HAZ to either side of the weld, and any base metal within the convex surface. All of the material within the convex surface has to be evaluated and compared to the acceptance criteria.
As for the situation where the specimen shifts to one side while bending, it can mean the bent sample is not acceptable for evaluation. If the sample shifts such that the entire HAZ is not within the bent portion of the sample, it must be discarded and a new sample made. It is for that reason longitudinal bends are used or a wrap around type fixture is used when dissimilar materials are welded and evaluated. Even the wrap around type fixtures are not fail safe unless the technician takes sufficient care in placement and securing the test sample. My wrap around testing machine has a bolt passing through the secured end so that the bend sample can not shift from the proper location. I have to locate the drilled hole so that the weld is properly centered on the bend radius. I always cut one extra sample that is used to verify the proper location of the drilled hole. The first sample is not evaluated, it is used to simply verify the proper location of the drilled hole or let's me know that it has to be shifted closer to the weld or further away so that the weld is properly centered. The hole location can vary from one alloy combination to the next due to differences in ductility.
I have passed many aluminum bend tests to D1.2, D17.1, MIL-STD-1595, MIL-W-8604, as well as MIL-STD-2219 without a root side purge and without porosity problems.
Good luck. It appears you are on the right track.
Best regards - Al